A100621 Denominator of Cotesian number C(n,0).
1, 2, 6, 8, 90, 288, 840, 17280, 28350, 89600, 598752, 17418240, 63063000, 402361344000, 5003856000, 295206912, 976924698750, 342372925440000, 15209113920000, 5377993912811520000, 96852084769440, 89903156428800000, 37556196837868800000, 73570956727261593600000
Offset: 0
Examples
0, 1/2, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/63063000, 8181904909/402361344000, ... = A100620/A100621 = A002177/A002176 (the latter is not in lowest terms)
References
- Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
- See A002176 for further references.
Programs
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Mathematica
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}]; Table[cn[n, 0] // Denominator, {n, 0, 23}] (* Jean-François Alcover, Jan 16 2013 *)