A395085 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n,k) * (k+2)^(3*(n-k)) * a(k).

1, 8, 368, 53672, 18417792, 12448430408, 14734002979456, 28097178451227432, 81130289696299765760, 338100184090337099266952, 1957376783962527227924465664, 15260800458738673199736524993192, 156157190400027800782262515166445568

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..161

Formula

log(1+8*x) = Sum_{k>=1} a(k)/k * (x/(1 + (k+2)^3*x))^k.

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

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

Crossrefs

Column k=2 of A082170.

Sequence in context: A193878 A193187 A240380 * A038016 A221775 A381758

Adjacent sequences: A395082 A395083 A395084 * A395086 A395087 A395088

Keyword

nonn

Author

Seiichi Manyama, Apr 11 2026

Status

approved