A300489 a(n) = n! * [x^n] -log(1 - x)/(1 - n*x).

0, 1, 5, 65, 1766, 83674, 6124584, 639826452, 90328291248, 16558780949136, 3823322392154880, 1085461798576638240, 371610484248792556800, 150961314165968542273920, 71790302154674639506682880, 39506878580692178250399571200, 24909116615180033772524150937600

Offset: 0

Author

Ilya Gutkovskiy, Mar 07 2018

Keywords

• nonn

Examples

			The table of coefficients of x^k in expansion of e.g.f. -log(1 - x)/(1 - n*x) begins:
n = 0: (0), 1,   1,    2,     6,      24,  ...
n = 1:  0, (1),  3,   11,    50,     274,  ...
n = 2:  0,  1,  (5),  32,   262,    2644,  ...
n = 3:  0,  1,   7,  (65),  786,   11814,  ...
n = 4:  0,  1,   9,  110, (1766),  35344,  ...
n = 5:  0,  1,  11,  167,  3346,  (83674), ...
...
This sequence is the main diagonal of the table.
		

Crossrefs

Cf. A000254, A068102, A069015, A104150.

Programs

Mathematica

Table[n! SeriesCoefficient[-Log[1 - x]/(1 - n x), {x, 0, n}], {n, 0, 16}]
Join[{0}, Table[n! n^n Sum[1/(k n^k), {k, 1, n}], {n, 1, 16}]]

PARI

a(n) = n!*n^n*sum(i=1, n, 1/(i*n^i)); \\ Altug Alkan, Mar 08 2018

Formula

a(n) = n!*n^n*Sum_{k=1..n} 1/(k*n^k).