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A186262 Expansion of 3F2( (2, 1/2, 3/2); (3, 4))(16 x). 2
1, 2, 9, 56, 420, 3564, 33033, 327184, 3413124, 37119160, 417733316, 4837527072, 57397642640, 695394516600, 8579210711625, 107541060458400, 1367139314643300, 17599273282621800, 229116465142280100, 3013124257920348000, 39991185556010816400 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified May 20 02:50 EDT 2019. Contains 323412 sequences. (Running on oeis4.)