A094073 - OEIS

%I #25 Oct 09 2023 11:18:14

%S 4,240,49938,24608160,23465221750,38341895571708,98780305524248572,

%T 377796303580335320432,2048907276496726375662702,

%U 15198414983297581845761672560,149768511689247547252666676150490

%N Coefficients arising in combinatorial field theory.

%H Vincenzo Librandi, <a href="/A094073/b094073.txt">Table of n, a(n) for n = 1..160</a>

%H P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, <a href="https://arxiv.org/abs/quant-ph/0405103">Some useful combinatorial formulae for bosonic operators</a>, arXiv:quant-ph/0405103, 2004-2006.

%H P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, <a href="https://doi.org/10.1063/1.1904161">Some useful combinatorial formulas for bosonic operators</a>, J. Math. Phys. 46, 052110 (2005) (6 pages).

%F a(n) = (2n)!*bell(2n)*coeff(exp(x*sinh(x)), x^(2n)). - _Emeric Deutsch_, Jan 22 2005

%p 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

%t a[n_] := (2n)! BellB[2n] SeriesCoefficient[Exp[x Sinh[x]], {x, 0, 2n}];

%t Table[a[n], {n, 1, 11}] (* _Jean-François Alcover_, Nov 11 2018 *)

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

%Y Cf. A000110.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 01 2004

%E More terms from _Emeric Deutsch_, Jan 22 2005