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

%I A002691 M4661 N1996 #37 Oct 13 2017 15:46:22
%S A002691 1,9,120,2100,45360,1164240,34594560,1167566400,44108064000,
%T A002691 1843717075200,84475764172800,4209708914611200,226676633863680000,
%U A002691 13114862387827200000,811372819726909440000,53449184499510159360000,3735154775612827607040000
%N A002691 a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.
%C A002691 Coefficients of orthogonal polynomials.
%D A002691 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002691 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002691 Alois P. Heinz, <a href="/A002691/b002691.txt">Table of n, a(n) for n = 0..150</a>
%H A002691 H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1955-0078498-1">Orthogonal polynomials arising in the evaluation of inverse Laplace transforms</a>, Math. Comp. 9 (1955), 164-177.
%H A002691 H. E. Salzer, <a href="/A000407/a000407.pdf">Orthogonal polynomials arising in the evaluation of inverse Laplace transforms</a>, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy]
%F A002691 E.g.f.: (1-x)/(1-4*x)^(5/2).
%F A002691 Conjecture: a(n) +4*(-n-1)*a(n-1) +4*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Jun 07 2013
%p A002691 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
%t A002691 Join[{1},Table[(n+2)(2n+1)(2n-1)!/(n-1)!,{n,15}]] (* _Harvey P. Dale_, Jun 09 2011 *)
%o A002691 (PARI) a(n)=(n+2)*(2*n+1)*(2*n-1)!/(n-1)!
%Y A002691 Cf. A002690.
%K A002691 nonn,easy,nice
%O A002691 0,2
%A A002691 _N. J. A. Sloane_
%E A002691 Edited by _Ralf Stephan_, Mar 21 2004