A355465 Expansion of Sum_{k>=0} (k^k * x/(1 - k^k * x))^k.

1, 1, 17, 19812, 4296562388, 298027622009561768, 10314429455106223377205859112, 256923580408437742134605162130019436138968, 6277101736867794060924264576844540796924098543875220742528

Offset

0,3

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = Sum_{k=1..n} k^(k*n) * binomial(n-1,k-1) for n > 0.

Prog

(PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x/(1-k^k*x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(k*n)*binomial(n-1, k-1)));

Crossrefs

Cf. A349886, A355466.

Sequence in context: A308670 A308571 A283719 * A134360 A171687 A178050

Adjacent sequences: A355462 A355463 A355464 * A355466 A355467 A355468

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2022

Status

approved