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A094074 Coefficients arising in combinatorial field theory. 1
1, 5, 129, 7485, 755265, 116338005, 25263540225, 7328358482445, 2730934406225025, 1269262202389906725, 718835160819268317825, 486853691847850902700125, 388278919916351519293663425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..225

P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Some useful combinatorial formulas 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).

A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory, arXiv:quant-ph/0409152, 2004.

FORMULA

a(n) = (2n)!/(2^n*n!) * h(2n, 2), with h(n, x) the polynomials in A099174.

E.g.f.: Sum_{n>=0} a(n)*x^(2n)/(2n)! = (1-x^2)^(-1/2) * exp(2x^2/(1-x^2)).

MATHEMATICA

a[n_] := (2n)! SeriesCoefficient[(1-x^2)^(-1/2) Exp[2x^2/(1-x^2)], {x, 0, 2n}];

Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 11 2018 *)

CROSSREFS

Equals A001147(n) * A093620(n).

Cf. A000085, A005425, A094071, A094072, A094073.

Sequence in context: A316392 A277259 A230303 * A012218 A012136 A012022

Adjacent sequences: A094071 A094072 A094073 * A094075 A094076 A094077

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 01 2004

EXTENSIONS

Edited and extended by Ralf Stephan, Oct 14 2004

STATUS

approved

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Last modified November 29 09:49 EST 2022. Contains 358423 sequences. (Running on oeis4.)