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}]
A336436
a(0) = 0; a(n) = ((n-1)!)^3 + (1/n) * Sum_{k=1..n-1} (binomial(n,k) * (n-k-1)!)^3 * k * a(k).
Original entry on oeis.org
0, 1, 5, 107, 6020, 701424, 146665984, 50005133576, 25952660212352, 19469692241358336, 20277424971134267904, 28384315863525074792448, 52002222667299924427689984, 121958564445078246232792363008, 359324017883943122680656621023232
Offset: 0
-
a[0] = 0; a[n_] := a[n] = ((n - 1)!)^3 + (1/n) Sum[(Binomial[n, k] (n - k - 1)!)^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[-Log[1 - Sum[x^k/k^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3
Showing 1-2 of 2 results.