This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112035 #18 Jan 05 2025 19:51:38
%S A112035 0,8,540,42576,3675000,334595040,31539372732,3046472028320,
%T A112035 299666635774704,29894793786770040,3016010007220052700,
%U A112035 307083034957464057600,31506217163866419507000,3253427167078021753747200,337821983730064508845772700,35246436592815103238009282880
%N A112035 a(n) = Sum_{k=0..n} k*C(n,k)^2*C(n+k,k)^3, where C := binomial.
%H A112035 C. Elsner, <a href="https://web.archive.org/web/2024*/https://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 A112035 Table[Sum[k*Binomial[n, k]^2*Binomial[n + k, k]^3, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 10 2021 *)
%o A112035 (PARI) a(n) = sum(k=0, n, k*binomial(n,k)^2*binomial(n+k,k)^3); \\ _Michel Marcus_, Mar 10 2016
%Y A112035 Cf. A055246 (indices where not multiple of 3), A112036.
%K A112035 nonn
%O A112035 0,2
%A A112035 _N. J. A. Sloane_, Nov 28 2005