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, Some useful combinatorial formulae for bosonic operators, arXiv:quant-ph/0405103, 2004-2006.

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