OFFSET
1,1
REFERENCES
Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Colin Barker,Table of n, a(n) for n = 1..1000
Cornelius Lanczos,Applied Analysis.(Annotated scans of selected pages)
Simon Plouffe,Approximations de séries génératrices et quelques conjectures,Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe,1031 Generating Functions,Appendix to Thesis, Montreal, 1992.
Index entries for linear recurrences with constant coefficients,signature (12,-48,64).
FORMULA
a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3). -Colin Barker,Jun 15 2015
a(n) = 1/2*Sum_{k = 0..2*n} k^2*binomial(2*n,k). Cf.A002699.-Peter Bala,Apr 09 2017
FromAmiram Eldar,Feb 17 2023: (Start)
Sum_{n>=1} 1/a(n) = 8 + 8*log(2) - 12*log(3).
Sum_{n>=1} (-1)^(n+1)/a(n) = 16*arctan(1/2) + 4*log(5/4) - 8. (End)
MAPLE
A002700:=-(3+4*z)/(4*z-1)**3; #Simon Plouffein his 1992 dissertation.
MATHEMATICA
Table[n*(2*n+1)*2^(2*n-2), {n, 1, 30}] (*Vaclav Kotesovec,Jun 03 2014 *)
LinearRecurrence[{12, -48, 64}, {3, 40, 336}, 30] (*Harvey P. Dale,May 17 2018 *)
PROG
(PARI) Vec(-x*(4*x+3)/(4*x-1)^3 + O(x^30)) \\Colin Barker,Jun 15 2015
(Magma) [4^(n-1)*n*(2*n+1): n in [1..30]]; //G. C. Greubel,Jul 23 2019
(Sage) [4^(n-1)*n*(2*n+1) for n in (1..30)] #G. C. Greubel,Jul 23 2019
(GAP) List([1..30], n-> 4^(n-1)*n*(2*n+1)); #G. C. Greubel,Jul 23 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved