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 A112036 #12 Jan 05 2025 19:51:38 %S A112036 0,2,36,708,13800,275010,5546016,112928648,2316836304,47818490310, %T A112036 991809240180,20655287811972,431646101898336,9046910585978538, %U A112036 190096907348726280,4003238051096801040,84468326787457833888,1785362928126983779374,37794508394454024115212,801183789256961484235340 %N A112036 a(n) = Sum_{k=0..n} k*C(n,k)^3*C(n+k,k), where C := binomial. %H A112036 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>, Fib. Q., 43,1 (2005), 31-45. %t A112036 Table[Sum[k*Binomial[n, k]^3*Binomial[n + k, k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 10 2021 *) %o A112036 (PARI) a(n) = sum(k=0, n, k*binomial(n, k)^3*binomial(n+k,k)); \\ _Michel Marcus_, Mar 10 2016 %Y A112036 Cf. A112035. %K A112036 nonn %O A112036 0,2 %A A112036 _N. J. A. Sloane_, Nov 28 2005