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A100646
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Denominator of Cotesian number C(n,2).
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3
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6, 8, 15, 144, 280, 640, 14175, 2240, 199584, 87091200, 875875, 22353408000, 5003856000, 229605376, 10854718875, 941525544960000, 1013940928000, 3064383995904000, 82324272054024, 2996771880960000, 255484332230400000, 809280523999877529600000, 5699209469078125
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OFFSET
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2,1
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REFERENCES
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Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
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LINKS
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EXAMPLE
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1/6, 3/8, 2/15, 25/144, 9/280, 49/640, -464/14175, 27/2240, -16175/199584, -3237113/87091200, -105387/875875, -1737125143/22353408000, -770720657/5003856000, -25881785/229605376,... =A100645/A100646=A002179/A002176(the latter not being in lowest terms)
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MATHEMATICA
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cn[n_, 0]:= Sum[n^j*StirlingS1[n, j]/(j+1), {j, 1, n+1}]/n!; cn[n_, n_]:= cn[n, 0]; cn[n_, k_]:= 1/n!*Binomial[n, k]*Sum[n^(j+m)*StirlingS1[k, j]* StirlingS1[n-k, m]/((m+1)*Binomial[j+m+1, m+1]), {m, 1, n}, {j, 1, k+1}]; a[n_]:= Denominator[cn[n, 2]]; Table[a[n], {n, 2, 24}] (*Jean-François Alcover,Oct 08 2013 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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