A352069 Expansion of e.g.f. 1 / (1 + log(1 - 3*x) / 3).

1, 1, 5, 42, 492, 7374, 134478, 2887128, 71281656, 1988802720, 61860849552, 2121993490176, 79566300371952, 3237181141173264, 142019158472311248, 6682603650677875584, 335698708873243355136, 17930674324049810882688, 1014685181110897126616448, 60641642160287342580586752

Offset: 0

Author

Ilya Gutkovskiy, Mar 02 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A032031, A087674, A227917, A255927, A352071.

Programs

Mathematica

nmax = 19; CoefficientList[Series[1/(1 + Log[1 - 3 x]/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! (-3)^(n - k), {k, 0, n}], {n, 0, 19}]

PARI

my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-3*x)/3))) \\ Michel Marcus, Mar 02 2022

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * (-3)^(n-k).

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

a(n) ~ n! * 3^(n+1) * exp(3*n) / (exp(3) - 1)^(n+1). - Vaclav Kotesovec, Mar 03 2022