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 A336440 a(n) = (n!)^n * [x^n] -log(1 + Sum_{k>=1} (-x)^k / k^n). 3
 0, 1, 1, 53, 65656, 4306202624, 21250781850448256, 11198392471992778644752768, 847058443993661249394101877997568000, 11916672812223274564264480372420932763474540363776, 39215070895580530235582705162664184972620228444352744200981184512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..10. MATHEMATICA Table[(n!)^n SeriesCoefficient[-Log[1 + Sum[(-x)^k/k^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}] b[n_, k_] := If[n == 0, 0, (-1)^(n + 1) ((n - 1)!)^k - (1/n) Sum[(-1)^(n - j) (Binomial[n, j] (n - j - 1)!)^k j b[j, k], {j, 1, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}] CROSSREFS Cf. A089064, A336437, A336438, A336439. Sequence in context: A169595 A183793 A367766 * A368298 A145332 A087530 Adjacent sequences: A336437 A336438 A336439 * A336441 A336442 A336443 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 21 2020 STATUS approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)