A094073 Coefficients arising in combinatorial field theory.

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

Offset

1,1

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).

Formula

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

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 *)

Crossrefs

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

Cf. A000110.

Sequence in context: A013953 A051753 A323996 * A137342 A152793 A042769

Adjacent sequences: A094070 A094071 A094072 * A094074 A094075 A094076

Keyword

nonn

Author

N. J. A. Sloane, May 01 2004

Extensions

More terms from Emeric Deutsch, Jan 22 2005

Status

approved