2,2

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

Vincenzo Librandi, Table of n, a(n) for n = 2..100

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)

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 *)

Cf. A100646.

See A002176 for further references. A diagonal of A100640/A100641.

Sequence in context: A228772 A165714 A090883 * A132960 A009574 A059422

Adjacent sequences: A100642 A100643 A100644 * A100646 A100647 A100648

sign,frac

N. J. A. Sloane, Dec 05 2004

approved