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

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%I A355465 #9 Jul 03 2022 13:56:25
%S A355465 1,1,17,19812,4296562388,298027622009561768,
%T A355465 10314429455106223377205859112,
%U A355465 256923580408437742134605162130019436138968,6277101736867794060924264576844540796924098543875220742528
%N A355465 Expansion of Sum_{k>=0} (k^k * x/(1 - k^k * x))^k.
%F A355465 a(n) = Sum_{k=1..n} k^(k*n) * binomial(n-1,k-1) for n > 0.
%o A355465 (PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x/(1-k^k*x))^k))
%o A355465 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(k*n)*binomial(n-1, k-1)));
%Y A355465 Cf. A349886, A355466.
%K A355465 nonn
%O A355465 0,3
%A A355465 _Seiichi Manyama_, Jul 03 2022