A112035 a(n) = Sum_{k=0..n} k*C(n,k)^2*C(n+k,k)^3, where C := binomial.

0, 8, 540, 42576, 3675000, 334595040, 31539372732, 3046472028320, 299666635774704, 29894793786770040, 3016010007220052700, 307083034957464057600, 31506217163866419507000, 3253427167078021753747200, 337821983730064508845772700, 35246436592815103238009282880

Offset: 0

Author

N. J. A. Sloane, Nov 28 2005

Keywords

• nonn

Links

• C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fibonacci Quarterly, 43,1 (2005), 31-45.

Crossrefs

Cf. A055246 (indices where not multiple of 3), A112036.

Programs

Mathematica

Table[Sum[k*Binomial[n, k]^2*Binomial[n + k, k]^3, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)

PARI

a(n) = sum(k=0, n, k*binomial(n,k)^2*binomial(n+k,k)^3); \\ Michel Marcus, Mar 10 2016