A354941 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-2)^(n-k).

1, -1, -10, -2, 488, 4088, -9968, -730480, -9751936, -11540096, 2480655104, 62522038016, 680469314560, -8292439149568, -606011029669888, -15765339965278208, -183530875864317952, 4164677242501038080, 318357069130977181696, 10359690304436314505216, 176911847384965046337536

Offset: 0

Author

Ilya Gutkovskiy, Jun 12 2022

Keywords

• sign

Crossrefs

Cf. A000023, A274246, A295382, A343840, A354942.

Programs

Mathematica

Table[Sum[Binomial[n, k]^3 k! (-2)^(n - k), {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-2)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3

PARI

a(n) = sum(k=0, n, binomial(n,k)^3 * k! * (-2)^(n-k)); \\ Michel Marcus, Jun 12 2022

Formula

Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} (-2)^n * x^n / n!^3.