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%I #5 Feb 07 2020 20:50:23
%S 1,1,6,47,493,6446,101009,1846631,38617674,909844075,23858239469,
%T 689399172870,21769608499937,745964574859679,27570932237831874,
%U 1093403260892542195,46315049663202237389,2087041161850908432022,99691702658041778953249,5031814773759672418067623
%N a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1) * a(n-k).
%F G.f.: 1 - 1 / (1 + Sum_{k>=1} k^(k-1) * x^k).
%t a[n_] := a[n] = n^(n - 1) - Sum[k^(k - 1) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]
%t nmax = 20; CoefficientList[Series[1 - 1/(1 + Sum[k^(k - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x] // Rest
%Y Cf. A000169, A003319, A088342, A296715, A332239.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Feb 07 2020
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