A364520 a(n) = (7*n)!*(n/2)!/((7*n/2)!*(n)!*(3*n)!).

1, 64, 12012, 2621440, 608435100, 146028888064, 35794148650260, 8901646138474496, 2237242000722428700, 566823049100850626560, 144520856111821003326512, 37036782455383679028953088, 9531607276865293630675462980, 2461693334077582876433071472640

Offset

0,2

Comments

Row 4 of A364519.

Links

Paolo Xausa, Table of n, a(n) for n = 0..400

Formula

a(n) = [x^(3*n)] ( (1 + x)^7/(1 - x) )^n.

a(n) = Sum_{j = 0..3*n} binomial(7*n, j)*binomial(4*n-j-1, 3*n-j).

a(n) = binomial(4*n-1, 3*n) * hypergeom([-7*n, -3*n], [1 - 4*n], -1) for n >= 2.

a(n) ~ c^n * 1/sqrt(6*Pi*n) where c = (14/3)^3*sqrt(7).

P-recursive: a(n) = 448*(7*n-1)*(7*n-3)*(7*n-5)*(7*n-9)*(7*n-11)*(7*n-13)/(3*n*(3*n-1)*(3*n-2)*(3*n-3)*(3*n-4)*(3*n-5)) * a(n-2) with a(0) = 1 and a(1) = 64.

The generating function is an algebraic function over the field of rational functions Q(x).

Maple

seq( simplify((7*n)!*(n/2)!/((7*n/2)!*(n)!*(3*n)!)),  n = 0..15);

Mathematica

A364520[n_]:=(7n)!(n/2)!/((7n/2)!n!(3n)!); Array[A364520, 15, 0] (* Paolo Xausa, Oct 05 2023 *)

Prog

(Python)
from math import factorial
from sympy import factorial2
def A364520(n): return int((factorial(7*n)*factorial2(n)<<(3*n))//(factorial2(7*n)*factorial(n)*factorial(3*n))) # Chai Wah Wu, Aug 13 2023

Crossrefs

Cf. A276098, A364519.

Sequence in context: A268055 A268078 A202548 * A209779 A220300 A316485

Adjacent sequences: A364517 A364518 A364519 * A364521 A364522 A364523

Keyword

nonn,easy

Author

Peter Bala, Aug 09 2023

Status

approved