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 A336437 a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / (k!)^n). 3

%I

%S 0,1,3,100,104585,5781843126,25450069471437282,

%T 12456703705462747095073458,900677059707267544414220026068619393,

%U 12337778954350678368447638232258657486399628887370,39982077640755835496555968029419604779794754953051698069276656138

%N a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / (k!)^n).

%t Table[(n!)^n SeriesCoefficient[-Log[1 - Sum[x^k/(k!)^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]

%t b[n_, k_] := If[n == 0, 0, 1 + (1/n) Sum[Binomial[n, j]^k j b[j, k], {j, 1, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]

%Y Cf. A000629, A102223, A326321, A336427, A336438, A336439, A336440.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 21 2020

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)