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}]
A336438
a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / k^n).
Original entry on oeis.org
0, 1, 3, 107, 109720, 5916402624, 25690641168448256, 12501662072725447325457536, 901886074956174349048867091963183104, 12343856662712388173832816538241443833756015132672, 39989244654801819205752864236178211163455535276138236680981184512
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, ((n - 1)!)^k + (1/n) Sum[(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}]
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}]
A336831
a(n) = (n!)^n * [x^n] exp(-Sum_{k>=1} (-x)^k / (k!)^n).
Original entry on oeis.org
1, 1, 1, 10, 4359, 91406876, 111657668637280, 11436881770074767723291, 137560155520600195617494951186559, 260122627893213770028102613184254361777327032, 99781796293430843492956500115058179262448159117567276656136
Offset: 0
-
Table[(n!)^n SeriesCoefficient[Exp[-Sum[(-x)^k/(k!)^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
b[n_, k_] := b[n, k] = If[n == 0, 1, -Sum[(-1)^(n - j) Binomial[n, j]^k (n - j) b[j, k], {j, 0, n - 1}]/n]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
Showing 1-4 of 4 results.