A000559 Generalized Stirling numbers of second kind. (Formerly M4858 N2076)

1, 12, 110, 945, 8092, 70756, 638423, 5971350, 57996774, 585092607, 6128147610, 66579524648, 749542556193, 8733648533696, 105203108066962, 1308549777461505, 16787682400875456, 221901108871482760, 3018891886411332135, 42230736603244134242

Offset

3,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 3..100

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, arXiv:quant-ph/0402027, 2004.

R. Fray, A generating function associated with the generalized Stirling numbers, Fib. Quart. 5 (1967), 356-366.

Formula

E.g.f.: (1/3!)*(exp(exp(x)-1)-1)^3. - Vladeta Jovovic, Sep 28 2003

a(n) = Sum_{k=0..n} Stirling2(n,k)*Stirling2(k,3).

Mathematica

nn = 23; t = Range[0, nn]! CoefficientList[Series[1/6*(Exp[Exp[x] - 1] - 1)^3, {x, 0, nn}], x]; Drop[t, 3] (* T. D. Noe, Aug 10 2012 *)

Crossrefs

Cf. A000558, A046817.

Sequence in context: A177071 A081183 A069294 * A037714 A037616 A048532

Adjacent sequences: A000556 A000557 A000558 * A000560 A000561 A000562

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson, Jan 13 2000

Status

approved