A000559 Generalized Stirling numbers of second kind.

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

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Crossrefs

Column k=3 of A130191.

Cf. A000558, A046817.

Programs

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 *)

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).

Extensions

More terms from David W. Wilson, Jan 13 2000