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

0,3

Links

Table of n, a(n) for n=0..13.

Formula

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

Prog

(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));

Crossrefs

Cf. A000045, A360592, A360684.

Cf. A355463.

Sequence in context: A237929 A227258 A027686 * A357825 A187647 A322645

Adjacent sequences: A360693 A360694 A360695 * A360697 A360698 A360699

Keyword

nonn

Author

Seiichi Manyama, Feb 16 2023

Status

approved