A295468 a(n) = (30*n)!*(5*n)!*(3*n)!*(2*n)!/((15*n)!*(10*n)!*(8*n)!*(6*n)!*n!).

1, 2772725670, 40337629723514950470, 671214073076279711920414071900, 11815915461993730897935386470911734090310, 214599520915474479942307452790907076147031402434420, 3975780607168011583140781349809187812166883920578195778723100

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Formula

G.f.: hypergeom([1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30], [1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8], 5189853515625/256*x).

a(n) = binomial(30*n,15*n)*binomial(15*n,5*n)*binomial(2*n,n)/(binomial(8*n,3*n)*binomial(6*n,n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(12*n) * 5^(10*n) / (2^(8*n+2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

a[n_] := (30*n)!*(5*n)!*(3*n)!*(2*n)!/((15*n)!*(10*n)!*(8*n)!*(6*n)!*n!); Array[a, 7, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295468(n): return comb(30*n, 15*n)*comb(15*n, 5*n)*comb(2*n, n)//(comb(8*n, 3*n)*comb(6*n, n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A327811 A327835 A384796 * A384550 A257913 A382684

Adjacent sequences: A295465 A295466 A295467 * A295469 A295470 A295471

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved