A092956 a(n) = (2*n+2)!/((n+2)*n!).

1, 8, 90, 1344, 25200, 570240, 15135120, 461260800, 15878903040, 609493248000, 25812039052800, 1195656969830400, 60138698780160000, 3264143527636992000, 190165504623494400000, 11836497605427855360000, 783921372659482337280000

Offset: 0

Author

Amarnath Murthy, Mar 25 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..350

Crossrefs

Row sums of A105725.

Cf. A092582.

Programs

Magma

[Factorial(n+1)*Binomial(2*n+2, n): n in [0..20]]; // G. C. Greubel, Aug 11 2022

Maple

seq((2*n+2)!/(n+2)/n!,n=0..17); # Emeric Deutsch
a:=n->sum(mul (j-k+n,j=1..n),k=1..n): seq(a(n),n=1..17); # Zerinvary Lajos, Jun 04 2007

Mathematica

Table[(2n+2)!/((n+2) n!), {n, 0, 16}] (* Bruno Berselli, Mar 06 2013 *)

Maxima

A092956(n):=(2*n+2)!/((n+2)*n!)$ makelist(A092956(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

SageMath

[factorial(n+1)*binomial(2*n+2,n) for n in (0..20)] # G. C. Greubel, Aug 11 2022

Formula

a(n) = Sum_{k=1..n+1} Gamma(n+1+k)/Gamma(k). - Bruno Berselli, Mar 06 2013

Let E(x) = Sum_{n>=0} a(n)*x^(2*n)/n!, then E(x) = 2- E(0,x), where E(k,x) = 1 - x^2*(k+1)/( x^2*(k+1) + (k + 1 -x^2)*(k + 2 -x^2)/E(k+1,x) ); (continued fraction). - Sergei N. Gladkovskii, Oct 21 2013

a(n) = A092582(2n+2, n+1). - Alois P. Heinz, Jun 19 2017

From G. C. Greubel, Aug 11 2022: (Start)

G.f.: Hypergeometric2F1([2,2,3/2], [3], 4*x).

E.g.f.: 4*x*Hypergeometric2F1([5/2,3], [4], 4*x) + Hypergeometric2F1([3/2,2], [3], 4*x). (End)

Extensions

More terms from Emeric Deutsch, Apr 18 2005

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007

More terms from Zerinvary Lajos, Jun 04 2007