A104674 a(n) = binomial(n+6, 6) * binomial(n+11, n).

1, 84, 2184, 30576, 286650, 2018016, 11435424, 54609984, 226972746, 840639800, 2824549728, 8730426432, 25099975992, 67725379008, 172768824000, 419252346240, 972796459635, 2167754048460, 4656656844840, 9674494830000, 19494107082450, 38192536324800, 72913023892800

Offset: 0

Author

Zerinvary Lajos, Apr 22 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+6,6)*C(0+11,0+0) = C(6,6)*C(11,0) = 1*1 = 1.
If n=8 then C(8+6,6)*C(8+11,8+0) = C(14,6)*C(19,8) = 3003*75582 = 226972746.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

Crossrefs

Cf. A062190.

Programs

Magma

A104674:= func< n | Binomial(n+6,n)*Binomial(n+11,n) >;
[A104674(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025

Mathematica

a[n_] := Binomial[n + 6, 6] * Binomial[n + 11, n]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)

PARI

a(n)={binomial(n+6, 6) * binomial(n+11, n)} \\ Andrew Howroyd, Nov 08 2019

SageMath

def A104674(n): return binomial(n+6,n)*binomial(n+11,n)
print([A104674(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025

Formula

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 33033*Pi^2 - 16431490141/50400.

Sum_{n>=0} (-1)^n/a(n) = 1171456*log(2)/105 - 11*Pi^2/2 - 1625274871/211680. (End)

G.f.: (1 + 66*x + 825*x^2 + 3300*x^3 + 4950*x^4 + 2772*x^5 + 462*x^6)/(1 - x)^18. - G. C. Greubel, Mar 01 2025

Extensions

a(8) corrected and terms a(9) and beyond from Andrew Howroyd, Nov 08 2019