A002691 a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!. (Formerly M4661 N1996)

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

Offset

0,2

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]

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

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 *)

Prog

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

Crossrefs

Cf. A002690.

Sequence in context: A167593 A214698 A024487 * A234320 A157930 A259836

Adjacent sequences: A002688 A002689 A002690 * A002692 A002693 A002694

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Edited by Ralf Stephan, Mar 21 2004

Status

approved