A295449 - OEIS

A295449

a(n) = (12*n)!*(2*n)!/((7*n)!*(4*n)!*(3*n)!).

1, 1320, 5883768, 30159472200, 163806801888376, 918503902622731320, 5255426168361638299800, 30493180338359901231171960, 178749192506567211692013235320, 1056050334837831740009828413441344, 6277811703390706059233733243310089768, 37506272066153520595120781707670683894800, 225005811874654647839031201018894323892255640

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

G.f.: hypergeom([1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], [1/7, 2/7, 3/7, 4/7, 5/7, 6/7], 5159780352/823543*x).

a(n) = binomial(12*n,5*n)*binomial(5*n,n)/binomial(3*n,n) = binomial(12*n,5*n)*binomial(7*n,3*n)/binomial(7*n,2*n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(18*n) * 3^(9*n) / (7^(7*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 23 2026

MATHEMATICA

a[n_] := (12*n)!*(2*n)!/((7*n)!*(4*n)!*(3*n)!); Array[a, 13, 0] (* Amiram Eldar, Feb 23 2026 *)

PROG

(Python)

from math import comb

def A295449(n): return comb(12*n, 5*n)*comb(5*n, n)//comb(3*n, n) # Chai Wah Wu, Feb 15 2026

CROSSREFS

Cf. A295431.

Sequence in context: A323802 A350612 A013641 * A092088 A068302 A139666

Adjacent sequences: A295446 A295447 A295448 * A295450 A295451 A295452

KEYWORD

nonn,easy

AUTHOR

Gheorghe Coserea, Nov 27 2017

STATUS

approved