A112036 a(n) = Sum_{k=0..n} k*C(n,k)^3*C(n+k,k), where C := binomial.

0, 2, 36, 708, 13800, 275010, 5546016, 112928648, 2316836304, 47818490310, 991809240180, 20655287811972, 431646101898336, 9046910585978538, 190096907348726280, 4003238051096801040, 84468326787457833888, 1785362928126983779374, 37794508394454024115212, 801183789256961484235340

Offset: 0

Author

N. J. A. Sloane, Nov 28 2005

Keywords

• nonn

Links

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

Crossrefs

Cf. A112035.

Programs

Mathematica

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

PARI

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