A355463 - OEIS

%I #20 Feb 16 2023 11:32:03

%S 1,1,2,10,131,5656,869097,490286392,1264458639313,12443651667592768,

%T 681538604797281047489,153070077563816488157872384,

%U 205935348854901274982393017521537,1352544986573612111579941739713633174912

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

%H Seiichi Manyama, <a href="/A355463/b355463.txt">Table of n, a(n) for n = 0..52</a>

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

%t Flatten[{1, Table[Sum[Binomial[n-1,k-1] * k^(k*(n-k)), {k,1,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Feb 16 2023 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^k*x))^k))

%o (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(k*(n-k))*binomial(n-1, k-1)));

%Y Cf. A193198, A193199, A349893, A355464.

%Y Cf. A080108, A355471, A355472.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 03 2022