OFFSET
0,2
COMMENTS
Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n), A094869(n), A094905(n), A094911(n), A094935(n) for x = 1, 2, 3, 4, 5, 6, 7, 8 respectively.
From Vaclav Kotesovec, Nov 19 2021: (Start)
In general, for k > 0, if e.g.f. = exp(k*x) / (1 - k*x)^(1/k), then a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * k^n / (Gamma(1/k) * exp(n-1) * n^(1 - 1/k)).
Equivalently, a(n) ~ n! * exp(1) * k^n / (Gamma(1/k) * n^(1 - 1/k)). (End)
FORMULA
a(n) = Sum_{k = 0..n} A046716(n, k)*9^k.
D-finite with recurrence a(n) +(-9*n-1)*a(n-1) +81*(n-1)*a(n-2)=0. - R. J. Mathar, Aug 20 2021
a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 9^n / (Gamma(1/9) * exp(n-1) * n^(8/9)). - Vaclav Kotesovec, Nov 19 2021
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[9x]/Surd[1-9x, 9], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 25 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jun 20 2004
STATUS
approved