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A359659 a(n) = Sum_{k=0..n} k^(k * (n-k+1)).

%I A359659 #18 Jan 12 2023 06:44:30
%S A359659 1,2,6,45,1051,88602,27121964,37004504305,198705527223757,
%T A359659 5595513387083114570,686714367475480207331582,
%U A359659 468422339816915120237104999421,1664212116512828935888786624225704855
%N A359659 a(n) = Sum_{k=0..n} k^(k * (n-k+1)).
%H A359659 Seiichi Manyama, <a href="/A359659/b359659.txt">Table of n, a(n) for n = 0..51</a>
%F A359659 G.f.: Sum_{k>=0} (k * x)^k/(1 - k^k * x).
%F A359659 G.f.: Sum_{k>=0} x^k/(1 - (k+1)^(k+1) * x).
%F A359659 a(n) = A349893(n+1) - 1.
%o A359659 (PARI) a(n) = sum(k=0, n, k^(k*(n-k+1)));
%o A359659 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^k*x)))
%o A359659 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k+1)^(k+1)*x)))
%Y A359659 Cf. A026898, A349893, A359658.
%Y A359659 Cf. A031971, A349836, A349883.
%Y A359659 Cf. A003101, A349882.
%K A359659 nonn
%O A359659 0,2
%A A359659 _Seiichi Manyama_, Jan 10 2023