A383929 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n, k) * (n-k)^(3*n).

1, 1, 60, 16626, 12640320, 20421928750, 60233972198400, 293230314199497444, 2192804991244707840000, 23869875368184417393486678, 362747302615636095725568000000, 7442995512384107947406685870219196, 200637069747857913587015560318156800000, 6945549555749361962465324588957867814958924

Offset: 0

Author

Vaclav Kotesovec, May 15 2025

Keywords

• nonn

Crossrefs

Cf. A002674, A298851, A383916, A383930.

Programs

Mathematica

Join[{1}, Table[Sum[(-1)^(n-k)*Binomial[2*n, n-k]*k^(3*n), {k, 0, n}], {n, 1, 15}]]

Formula

a(n) ~ 2^(2*n + 1/2) * r^(3*n + 1) * n^(3*n) / (sqrt(3 - r^2) * exp(3*n) * (r^2 - 1)^n), where r = 1.1647414545521878292908344008181647954486720209245020743652... is the root of the equation (1 + r)/(1 - r) = -exp(3/r).