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A003472
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a(n) = 2^(n-4)*C(n,4).
(Formerly M4718)
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27
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1, 10, 60, 280, 1120, 4032, 13440, 42240, 126720, 366080, 1025024, 2795520, 7454720, 19496960, 50135040, 127008768, 317521920, 784465920, 1917583360, 4642570240, 11142168576, 26528972800, 62704844800, 147220070400
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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4,2
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COMMENTS
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Number of 4D hypercubes in n-dimensional hypercube. -Henry Bottomley,Apr 14 2000
With four leading zeros, binomial transform of C(n,4). -Paul Barry,Apr 10 2003
If X_1, X_2,..., X_n is a partition of a 2n-set X into 2-blocks, then, for n>3, a(n) is equal to the number of (n+4)-subsets of X intersecting each X_i (i=1,2,...,n). -Milan Janjic,Jul 21 2007
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 796.
Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009, page 282.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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M. Abramowitz and I. A. Stegun, eds.,Handbook of Mathematical Functions,National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
C. W. Jones, J. C. P. Miller, J. F. C. Conn and R. C. Pankhurst,Tables of Chebyshev polynomialsProc. Roy. Soc. Edinburgh. Sect. A., Vol. 62, No. 2 (1946), pp. 187-203.
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FORMULA
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O.g.f.: x^4/(1-2*x)^5.
E.g.f.: exp(2*x)(x^4/4!) (with 4 leading zeros). (End)
a(n) = Sum_{i=4..n} binomial(i,4)*binomial(n,i). Example: for n=7, a(7) = 1*35 + 5*21 + 15*7 + 35*1 = 280. -Bruno Berselli,Mar 23 2018
Sum_{n>=4} 1/a(n) = 20/3 - 8*log(2).
Sum_{n>=4} (-1)^n/a(n) = 216*log(3/2) - 260/3. (End)
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MAPLE
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MATHEMATICA
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Table[2^(n-4) Binomial[n, 4], {n, 4, 50}] (* or *) LinearRecurrence[{10, -40, 80, -80, 32}, {1, 10, 60, 280, 1120}, 50] (*Harvey P. Dale,May 27 2017 *)
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PROG
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(Sage) [2^(n-4)*binomial(n, 4) for n in (4..30)] #G. C. Greubel,Aug 27 2019
(GAP) List([4..30], n-> 2^(n-4)*Binomial(n, 4)); #G. C. Greubel,Aug 27 2019
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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