A000559 - OEIS

%I M4858 N2076 #36 Jan 05 2025 19:51:31

%S 1,12,110,945,8092,70756,638423,5971350,57996774,585092607,6128147610,

%T 66579524648,749542556193,8733648533696,105203108066962,

%U 1308549777461505,16787682400875456,221901108871482760,3018891886411332135,42230736603244134242

%N Generalized Stirling numbers of second kind.

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

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

%H T. D. Noe, <a href="/A000559/b000559.txt">Table of n, a(n) for n = 3..100</a>

%H P. Blasiak, K. A. Penson and A. I. Solomon, <a href="https://arxiv.org/abs/quant-ph/0402027">The general boson normal ordering problem</a>, arXiv:quant-ph/0402027, 2004.

%H R. Fray, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/5-4/fray.pdf">A generating function associated with the generalized Stirling numbers</a>, Fib. Quart. 5 (1967), 356-366.

%F E.g.f.: (1/3!)*(exp(exp(x)-1)-1)^3. - _Vladeta Jovovic_, Sep 28 2003

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

%t 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 *)

%Y Cf. A000558, A046817.

%K nonn,easy

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_, Jan 13 2000