A360696 Expansion of Sum_{k>=0} (x * (1 + k^k * x))^k.

1, 1, 2, 9, 98, 3212, 428525, 165045051, 342128248388, 2522279110319003, 90930729844450829580, 17690430223837969605522024, 13516362920784209950583739768297, 79459280482613898608830749440741093093

Offset: 0

Author

Seiichi Manyama, Feb 16 2023

Keywords

• nonn

Crossrefs

Cf. A000045, A360592, A360684.

Cf. A355463.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(1+k^k*x))^k))

PARI

a(n) = sum(k=0, n\2, (n-k)^(k*(n-k))*binomial(n-k, k));

Formula

a(n) = Sum_{k=0..floor(n/2)} (n-k)^(k*(n-k)) * binomial(n-k,k).