A185247 Expansion of 3F2( (1/4,1/2,3/4); (4,6) )(256 x)

1, 1, 12, 330, 14300, 831402, 59491432, 4971783960, 468842704200, 48707547603000, 5478624954385440, 658555622357831640, 83752779737507765040, 11180459218164097480500, 1556759031871924444410000, 224927463853886185614776400, 33579302695870956078753329400, 5161336349665341660810732336600

Offset

0,3

Comments

Combinatorial interpretation welcome.

Links

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

Formula

D-finite with recurrence n*(n+5)*(n+3)*a(n) -8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022

From Vaclav Kotesovec, Feb 17 2024: (Start)

a(n) = 720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!).

a(n) ~ 45 * 2^(8*n + 7/2) / (Pi^(3/2) * n^(19/2)). (End)

Mathematica

CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {4, 6}, 256 x], {x, 0, 20}], x]
Table[720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!), {n, 0, 20}] (* Vaclav Kotesovec, Feb 17 2024 *)

Crossrefs

Sequence in context: A230817 A298245 A110101 * A368771 A009530 A159363

Adjacent sequences: A185244 A185245 A185246 * A185248 A185249 A185250

Keyword

nonn

Author

Olivier Gérard, Feb 15 2011

Status

approved