A295462 a(n) = (15*n)!*(2*n)!/((10*n)!*(6*n)!*n!).

1, 1001, 2731365, 8452632980, 27614258931525, 92994778322102376, 319323042934810327908, 1111423634892509277158820, 3907116913932203786698907205, 13840531451943824412017357524400, 49326067264186310295180241747943240, 176657291645522807951014259080005974280

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/10, 1/6, 3/10, 1/2, 7/10, 5/6, 9/10], 61509375/16384*x).

a(n) = binomial(15*n,5*n)*binomial(2*n,n)/binomial(6*n,n) = binomial(15*n,5*n)*binomial(7*n,n)/binomial(7*n,2*n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(9*n) * 5^(5*n) / (2^(14*n+1) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (15*n)!*(2*n)!/((10*n)!*(6*n)!*n!); Array[a, 12, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295462(n): return comb(15*n, 5*n)*comb(2*n, n)//comb(6*n, n) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A140927 A261544 A097659 * A143906 A215593 A204575

Adjacent sequences: A295459 A295460 A295461 * A295463 A295464 A295465

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved