OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=1..n} n^(n-k)*binomial(n,k)*k!*H(k), where H(k) is the k-th harmonic number.
EXAMPLE
The table of coefficients of x^k in expansion of e.g.f. -exp(n*x)*log(1 - x)/(1 - x) begins:
n = 0: (0), 1, 3, 11, 50, 274, ...
n = 1: 0, (1), 5, 23, 116, 669, ...
n = 2: 0, 1, (7), 41, 242, 1534, ...
n = 3: 0, 1, 9, (65), 452, 3229, ...
n = 4: 0, 1, 11, 95, (770), 6234, ...
n = 5: 0, 1, 13, 131, 1220, (11149), ...
...
This sequence is the main diagonal of the table.
MATHEMATICA
Table[n! SeriesCoefficient[-Exp[n x] Log[1 - x]/(1 - x), {x, 0, n}], {n, 0, 19}]
Table[Sum[n^(n - k) Binomial[n, k] k! HarmonicNumber[k], {k, 1, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 07 2018
STATUS
approved