A355463 Expansion of Sum_{k>=0} (x/(1 - k^k * x))^k.

1, 1, 2, 10, 131, 5656, 869097, 490286392, 1264458639313, 12443651667592768, 681538604797281047489, 153070077563816488157872384, 205935348854901274982393017521537, 1352544986573612111579941739713633174912

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..52

Formula

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

Mathematica

Flatten[{1, Table[Sum[Binomial[n-1, k-1] * k^(k*(n-k)), {k, 1, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 16 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^k*x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(k*(n-k))*binomial(n-1, k-1)));

Crossrefs

Cf. A193198, A193199, A349893, A355464.

Cf. A080108, A355471, A355472.

Sequence in context: A097928 A254431 A011838 * A336537 A118183 A134051

Adjacent sequences: A355460 A355461 A355462 * A355464 A355465 A355466

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2022

Status

approved