%I #14 Nov 19 2021 09:49:33
%S 1,9,89,1073,18321,476473,17484457,813648417,45054110369,
%T 2872362067433,206710159889529,16558892507010961,1460688620617834801,
%U 140655075719488236057,14678730623948132120009
%N E.g.f.: exp(8x)/(1-8x)^(1/8).
%C Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n), A094869(n), A094905(n), A094911(n) for x = 1, 2, 3, 4, 5, 6, 7 respectively.
%F a(n) = Sum_{k = 0..n} A046716(n, k)*8^k.
%F D-finite with recurrence: a(n) +(-8*n-1)*a(n-1) +64*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 15 2019
%F a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 8^n / (Gamma(1/8) * exp(n-1) * n^(7/8)). - _Vaclav Kotesovec_, Nov 19 2021
%t With[{nn=20},CoefficientList[Series[Exp[8x]/Surd[1-8x,8],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jan 25 2019 *)
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 18 2004