A295444 a(n) = (12*n)!*(2*n)!/((9*n)!*(4*n)!*n!).

1, 110, 28842, 8558480, 2679559018, 864609808860, 284430822189360, 94838361498813504, 31937586416482122090, 10837486229625098253938, 3699768692414430886979092, 1269247320827841357100956000, 437197260018920565848972207920, 151108564566619626342188272922000, 52379783376231201890753924949502656, 18202391389394546898846524075693898480

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

G.f.: hypergeom([1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 262144/729*x).

a(n) ~ 2^(18*n) / (3^(6*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

a(n) = binomial(12*n,3*n)*binomial(2*n,n)/binomial(4*n,n) = binomial(12*n,3*n)*binomial(5*n,n)/binomial(5*n,2*n). - Chai Wah Wu, Feb 15 2026

Mathematica

f[n_] := (12n)! (2n)!/((9n)! (4n)! n!); Array[f, 14, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12}, {1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, 262144/729 x], {x, 0, 13}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295444(n): return comb(12*n, 3*n)*comb(2*n, n)//comb(4*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A396062 A216786 A350320 * A295436 A375357 A246635

Adjacent sequences: A295441 A295442 A295443 * A295445 A295446 A295447

Keyword

nonn

Author

Gheorghe Coserea, Nov 23 2017

Status

approved