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A186264 Expansion of 3F2( (1, 3/2, 3/2); (3, 4))(16 x). 2
1, 3, 15, 98, 756, 6534, 61347, 613470, 6447012, 70526404, 797490876, 9271926888, 110380082000, 1341117996300, 16586474042475, 208360804638150, 2653858669601700, 34220809160653500, 446174168961282300, 5875592302944678600, 78078028942687784400 (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 (-3*(1 + 2*x - 2F1((-1/2, -1/2); (2))(16*x)))/(4*x^2).

a(n) = 3/((n+3)*(n+2)^2)*(2*n+2)!^2/(n+1)!^4 = 3/(n+3)* Catalan(n+1)^2. - Peter Bala, Mar 28 2018

MAPLE

seq(3/((n+3)*(n+2)^2)*binomial(2*n+2, n+1)^2, n = 0..20); # Peter Bala, Mar 28 2018

MATHEMATICA

CoefficientList[Series[HypergeometricPFQ[{1, 3/2, 3/2}, {3, 4}, 16*x], {x, 0, 20}],

  x]

CROSSREFS

Cf. A186262, A000108, A001246.

Sequence in context: A331610 A331618 A128081 * A140286 A199416 A046635

Adjacent sequences:  A186261 A186262 A186263 * A186265 A186266 A186267

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Feb 16 2011

STATUS

approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)