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

0,2

Links

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

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)

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 *)

Prog

(Maxima) A092956(n):=(2*n+2)!/((n+2)*n!)$ makelist(A092956(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Magma) [Factorial(n+1)*Binomial(2*n+2, n): n in [0..20]]; // G. C. Greubel, Aug 11 2022
(SageMath) [factorial(n+1)*binomial(2*n+2, n) for n in (0..20)] # G. C. Greubel, Aug 11 2022

Crossrefs

Row sums of A105725.

Cf. A092582.

Sequence in context: A323960 A187667 A331512 * A345876 A295623 A319174

Adjacent sequences: A092953 A092954 A092955 * A092957 A092958 A092959

Keyword

easy,nonn

Author

Amarnath Murthy, Mar 25 2004

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

Status

approved