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).

0, 1, 5, 107, 6020, 701424, 146665984, 50005133576, 25952660212352, 19469692241358336, 20277424971134267904, 28384315863525074792448, 52002222667299924427689984, 121958564445078246232792363008, 359324017883943122680656621023232

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^3 = -log(1 - Sum_{n>=1} x^n / n^3).

Mathematica

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

Crossrefs

Cf. A003713, A074708, A193420.

Sequence in context: A204110 A355955 A113056 * A318986 A220549 A210904

Adjacent sequences: A336433 A336434 A336435 * A336437 A336438 A336439

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2020

Status

approved