A112035 - OEIS

%I #16 Jul 10 2021 07:14:49

%S 0,8,540,42576,3675000,334595040,31539372732,3046472028320,

%T 299666635774704,29894793786770040,3016010007220052700,

%U 307083034957464057600,31506217163866419507000,3253427167078021753747200,337821983730064508845772700,35246436592815103238009282880

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

%H C. Elsner, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-5.pdf">On recurrence formulas for sums involving binomial coefficients</a>, Fibonacci Quarterly, 43,1 (2005), 31-45.

%t Table[Sum[k*Binomial[n, k]^2*Binomial[n + k, k]^3, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 10 2021 *)

%o (PARI) a(n) = sum(k=0, n, k*binomial(n,k)^2*binomial(n+k,k)^3); \\ _Michel Marcus_, Mar 10 2016

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 28 2005