A332238 a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1) * a(n-k).

1, 1, 6, 47, 493, 6446, 101009, 1846631, 38617674, 909844075, 23858239469, 689399172870, 21769608499937, 745964574859679, 27570932237831874, 1093403260892542195, 46315049663202237389, 2087041161850908432022, 99691702658041778953249, 5031814773759672418067623

Offset: 1

Author

Ilya Gutkovskiy, Feb 07 2020

Keywords

• nonn

Crossrefs

Cf. A000169, A003319, A088342, A296715, A332239.

Programs

Mathematica

a[n_] := a[n] = n^(n - 1) - Sum[k^(k - 1) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]
nmax = 20; CoefficientList[Series[1 - 1/(1 + Sum[k^(k - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x] // Rest

Formula

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