A395084 - OEIS

%I #14 Apr 11 2026 14:10:00

%S 1,9,207,9342,709893,82305144,13598786979,3046304952000,

%T 890852599520937,330148878794554752,151400106169172860311,

%U 84247226510471621178624,55963455552493696700729325,43768977972154220816612831232,39828325972837703285466600268203

%N a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n,k) * (k+3)^(2*(n-k)) * a(k).

%H Seiichi Manyama, <a href="/A395084/b395084.txt">Table of n, a(n) for n = 0..220</a>

%F log(1+9*x) = Sum_{k>=1} a(k)/k * (x/(1 + (k+3)^2*x))^k.

%F 1 = Sum_{k>=0} a(k) * binomial(k+m-1,k) * x^k/(1 + (k+3)^2*x)^(k+m) for m >= 1.

%F 1 = Sum_{k>=0} a(k) * x^k/k! * exp(-(k+3)^2*x).

%Y Column k=3 of A082169.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 11 2026