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A185247
Expansion of 3F2( (1/4,1/2,3/4); (4,6) )(256 x)
1
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
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
KEYWORD
nonn
AUTHOR
Olivier Gérard, Feb 15 2011
STATUS
approved