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a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).
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%I #14 Dec 11 2021 04:29:26

%S 1,0,1,-3,-10,410,42985,-6527829,-24060996846,-6613442955828,

%T 3882375189467092921,235121650953066124724477,

%U -289337164954511885810252000250,-995208334663809003504695464745010282,13325880481925983143500510271865447222057073

%N a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).

%H Seiichi Manyama, <a href="/A349894/b349894.txt">Table of n, a(n) for n = 0..52</a>

%F G.f.: Sum_{k>=0} x^k/(1 + k^k * x).

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

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

%Y Cf. A349856, A349857, A349858, A349891, A349893.

%K sign

%O 0,4

%A _Seiichi Manyama_, Dec 04 2021