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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 01 2004
EXTENSIONS
Edited and extended by Ralf Stephan, Oct 14 2004
STATUS
approved