A094073 Coefficients arising in combinatorial field theory.

4, 240, 49938, 24608160, 23465221750, 38341895571708, 98780305524248572, 377796303580335320432, 2048907276496726375662702, 15198414983297581845761672560, 149768511689247547252666676150490

Offset: 1

Author

N. J. A. Sloane, May 01 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..160
• P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering, arXiv:quant-ph/0405103, 2004-2006. The title of this paper in the arXiv was later changed to "Some useful combinatorial formulas for bosonic operators"
• P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Some useful combinatorial formulas for bosonic operators, J. Math. Phys. 46, 052110 (2005) (6 pages).

Crossrefs

Cf. A000085, A005425, A094070, A094071, A094072, A094074.

Cf. A000110.

Programs

Maple

with(combinat): a:=n->bell(2*n)*(2*n)!*coeff(series(exp(x*sinh(x)), x=0,40), x^(2*n)): seq(a(n),n=1..13); # Emeric Deutsch, Jan 22 2005

Mathematica

a[n_] := (2n)! BellB[2n] SeriesCoefficient[Exp[x Sinh[x]], {x, 0, 2n}];
Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Nov 11 2018 *)

Formula

a(n) = (2n)!*bell(2n)*coeff(exp(x*sinh(x)), x^(2n)). - Emeric Deutsch, Jan 22 2005

Extensions

More terms from Emeric Deutsch, Jan 22 2005