cp's OEIS Frontend

A094074 Coefficients arising in combinatorial field theory.

%I A094074 #28 May 19 2025 16:03:46
%S A094074 1,5,129,7485,755265,116338005,25263540225,7328358482445,
%T A094074 2730934406225025,1269262202389906725,718835160819268317825,
%U A094074 486853691847850902700125,388278919916351519293663425
%N A094074 Coefficients arising in combinatorial field theory.
%H A094074 Vincenzo Librandi, <a href="/A094074/b094074.txt">Table of n, a(n) for n = 0..225</a>
%H A094074 P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, <a href="http://arXiv.org/abs/quant-ph/0405103">Combinatorial field theories via boson normal ordering</a>, 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"
%H A094074 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).
%H A094074 A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, <a href="https://arxiv.org/abs/quant-ph/0409152">A product formula and combinatorial field theory</a>, arXiv:quant-ph/0409152, 2004.
%F A094074 a(n) = (2n)!/(2^n*n!) * h(2n, 2), with h(n, x) the polynomials in A099174.
%F A094074 E.g.f.: Sum_{n>=0} a(n)*x^(2n)/(2n)! = (1-x^2)^(-1/2) * exp(2x^2/(1-x^2)).
%t A094074 a[n_] := (2n)! SeriesCoefficient[(1-x^2)^(-1/2) Exp[2x^2/(1-x^2)], {x, 0, 2n}];
%t A094074 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Nov 11 2018 *)
%Y A094074 Equals A001147(n) * A093620(n).
%Y A094074 Cf. A000085, A005425, A094071, A094072, A094073.
%K A094074 nonn
%O A094074 0,2
%A A094074 _N. J. A. Sloane_, May 01 2004
%E A094074 Edited and extended by _Ralf Stephan_, Oct 14 2004.