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A002691
a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.
(Formerly M4661 N1996)
5
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
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
KEYWORD
nonn,easy,nice
EXTENSIONS
Edited by Ralf Stephan, Mar 21 2004
STATUS
approved