A395084 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n,k) * (k+3)^(2*(n-k)) * a(k).

1, 9, 207, 9342, 709893, 82305144, 13598786979, 3046304952000, 890852599520937, 330148878794554752, 151400106169172860311, 84247226510471621178624, 55963455552493696700729325, 43768977972154220816612831232, 39828325972837703285466600268203

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..220

Formula

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

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

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

Crossrefs

Column k=3 of A082169.

Sequence in context: A307735 A266483 A203364 * A218887 A001535 A300136

Adjacent sequences: A395081 A395082 A395083 * A395085 A395086 A395087

Keyword

nonn

Author

Seiichi Manyama, Apr 11 2026

Status

approved