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a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.
(Formerly M4661 N1996)
5

%I M4661 N1996 #37 Oct 13 2017 15:46:22

%S 1,9,120,2100,45360,1164240,34594560,1167566400,44108064000,

%T 1843717075200,84475764172800,4209708914611200,226676633863680000,

%U 13114862387827200000,811372819726909440000,53449184499510159360000,3735154775612827607040000

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

%C Coefficients of orthogonal polynomials.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H Alois P. Heinz, <a href="/A002691/b002691.txt">Table of n, a(n) for n = 0..150</a>

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

%F Conjecture: a(n) +4*(-n-1)*a(n-1) +4*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Jun 07 2013

%p 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 Join[{1},Table[(n+2)(2n+1)(2n-1)!/(n-1)!,{n,15}]] (* _Harvey P. Dale_, Jun 09 2011 *)

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

%Y Cf. A002690.

%K nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _Ralf Stephan_, Mar 21 2004