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

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A193198, A193199, A349893, A355464.

Cf. A080108, A355471, A355472.

Programs

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 *)

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)));

Formula

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