A002691 a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.

1, 9, 120, 2100, 45360, 1164240, 34594560, 1167566400, 44108064000, 1843717075200, 84475764172800, 4209708914611200, 226676633863680000, 13114862387827200000, 811372819726909440000, 53449184499510159360000, 3735154775612827607040000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Coefficients of orthogonal polynomials.

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150
• H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.
• H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy]

Crossrefs

Cf. A002690.

Programs

Maple

with(combstruct): a:=n-> add((count(Permutation(n*2+1), size=n+1)), j=0..n+1)/2: seq(a(n), n=0..16); # Zerinvary Lajos, May 03 2007

Mathematica

Join[{1},Table[(n+2)(2n+1)(2n-1)!/(n-1)!,{n,15}]] (* Harvey P. Dale, Jun 09 2011 *)

PARI

a(n)=(n+2)*(2*n+1)*(2*n-1)!/(n-1)!

Formula

E.g.f.: (1-x)/(1-4*x)^(5/2).

Conjecture: a(n) +4*(-n-1)*a(n-1) +4*(-2*n+1)*a(n-2)=0. - R. J. Mathar, Jun 07 2013

Extensions

Edited by Ralf Stephan, Mar 21 2004