A336439
a(n) = (n!)^n * [x^n] -log(Sum_{k>=0} (-x)^k / (k!)^n).
Original entry on oeis.org
0, 1, 1, 46, 63111, 4226436876, 21095962423437280, 11165885881625823212655540, 846105231095934499366980692096995455, 11911559696594230804398683820096471009503594129080, 39208751872375132639833577214095359308827747721266594509276656136
Offset: 0
-
Table[(n!)^n SeriesCoefficient[-Log[Sum[(-x)^k/(k!)^n, {k, 0, n}]], {x, 0, n}], {n, 0, 10}]
b[n_, k_] := If[n == 0, 0, (-1)^(n + 1) - (1/n) Sum[(-1)^(n - j) Binomial[n, j]^k j b[j, k], {j, 1, n - 1}]];a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
A336437
a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / (k!)^n).
Original entry on oeis.org
0, 1, 3, 100, 104585, 5781843126, 25450069471437282, 12456703705462747095073458, 900677059707267544414220026068619393, 12337778954350678368447638232258657486399628887370, 39982077640755835496555968029419604779794754953051698069276656138
Offset: 0
-
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 + (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}]
A336440
a(n) = (n!)^n * [x^n] -log(1 + Sum_{k>=1} (-x)^k / k^n).
Original entry on oeis.org
0, 1, 1, 53, 65656, 4306202624, 21250781850448256, 11198392471992778644752768, 847058443993661249394101877997568000, 11916672812223274564264480372420932763474540363776, 39215070895580530235582705162664184972620228444352744200981184512
Offset: 0
-
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}]
Showing 1-3 of 3 results.