A295432 - OEIS

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A295432

a(n) = (12*n)!*(3*n)!*(2*n)!/((6*n)!*(6*n)!*(4*n)!*n!).

1, 462, 579462, 825012300, 1240292449350, 1922257130698212, 3037843525927941276, 4866407206411278522456, 7873830606510488097067590, 12837724391783995395083457780, 21058175422921386792478888300212, 34712605923460405627194955063564200

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

G.f.: hypergeom([1/12, 5/12, 7/12, 11/12], [1/6, 1/2, 5/6], 1728*x).

a(n) = a(n-1)*6*(12*n - 1)*(12*n - 5)*(12*n - 7)*(12*n - 11)/(n*(2*n - 1)*(6*n - 1)*(6*n - 5)). - Neven Sajko, Jul 22 2023

MATHEMATICA

Array[(12 #)!*(3 #)!*(2 #)!/((6 #)!*(6 #)!*(4 #)!*#!) &, 12, 0] (* Michael De Vlieger, Nov 23 2017 *)

CoefficientList[ Series[ HypergeometricPFQ[{1/12, 5/12, 7/12, 11/12}, {1/6, 1/2, 5/6}, 1728 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

CROSSREFS