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

0,2

Links

Table of n, a(n) for n=0..15.

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A216353 A145182 A089671 * A200706 A266207 A027536

Adjacent sequences: A112032 A112033 A112034 * A112036 A112037 A112038

Keyword

nonn

Author

N. J. A. Sloane, Nov 28 2005

Status

approved