A186262 Expansion of 3F2( 2, 1/2, 3/2; 3, 4;16 x).

1, 2, 9, 56, 420, 3564, 33033, 327184, 3413124, 37119160, 417733316, 4837527072, 57397642640, 695394516600, 8579210711625, 107541060458400, 1367139314643300, 17599273282621800, 229116465142280100, 3013124257920348000, 39991185556010816400

Offset

0,2

Comments

Combinatorial interpretation welcome.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f. is equivalent to (-1 + 2F1(-3/2,-1/2;2;16*x) - 6*x*2F1(-1/2,1/2;3;16*x) )/(4*x^2).

a(n) = C(2*n,n)*C(2*n+2,n)/C(n+3,3). - Vaclav Kotesovec, Oct 28 2012

D-finite with recurrence +n*(n+3)*(n+2)*a(n) -4*(2*n+1)*(2*n-1)*(n+1)*a(n-1)=0. - R. J. Mathar, Feb 08 2021

Mathematica

CoefficientList[Series[HypergeometricPFQ[{2, 1/2, 3/2}, {3, 4}, 16*x], {x, 0, 20}], x]
Table[Binomial[2*n, n]*Binomial[2*n+2, n]/Binomial[n+3, 3], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)

Crossrefs

Close to A138740.

Sequence in context: A081004 A198953 A212392 * A138740 A276370 A292809

Adjacent sequences: A186259 A186260 A186261 * A186263 A186264 A186265

Keyword

nonn,easy

Author

Olivier Gérard, Feb 16 2011

Status

approved