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A100645
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Numerator of Cotesian number C(n,2).
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2
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1, 3, 2, 25, 9, 49, -464, 27, -16175, -3237113, -105387, -1737125143, -770720657, -25881785, -1997012608, -135505859252213, -214182958293, -528114253960241, -19467909708875, -595278405326437, -66462260889140083, -180690496141440384775397, -1610254561193224
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OFFSET
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2,2
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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_] := Numerator[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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sign,frac
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AUTHOR
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STATUS
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approved
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