login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.

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-Fran├žois Alcover, Nov 11 2018 *)

CROSSREFS

Equals A001174(n) * A005425(n).

Cf. A000085, A005425, A094065-.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)