A328811 a(n) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^n.

1, 1, 3, 31, 1255, 161671, 75481581, 121338954577, 734884394666535, 15970479086714049751, 1347242827078365957146473, 415839472158527880691583531617, 507266883682599825619985300960971525, 2284735689605775548174387143718048664963601

Offset: 0

Author

Seiichi Manyama, Oct 28 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..59

Crossrefs

Main diagonal of A328747.

Cf. A167010, A328810.

Programs

Mathematica

Table[Sum[(-1)^(n-i)*Binomial[n, i]*Sum[Binomial[i, j]^n, {j, 0, i}], {i, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Oct 28 2019 *)

PARI

{a(n) = sum(i=0, n, (-1)^(n-i)*binomial(n, i)*sum(j=0, i, binomial(i, j)^n))}

Formula

a(n) ~ A167010(n). - Vaclav Kotesovec, Oct 28 2019