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Denominator of Cotesian number C(n,0).
10

%I #6 Jan 16 2013 09:08:24

%S 1,2,6,8,90,288,840,17280,28350,89600,598752,17418240,63063000,

%T 402361344000,5003856000,295206912,976924698750,342372925440000,

%U 15209113920000,5377993912811520000,96852084769440,89903156428800000,37556196837868800000,73570956727261593600000

%N Denominator of Cotesian number C(n,0).

%D Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.

%D See A002176 for further references.

%e 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)

%t 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 *)

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Dec 04 2004