A352071 Expansion of e.g.f. 1 / (1 + log(1 - 4*x) / 4).

1, 1, 6, 62, 904, 16984, 390128, 10586736, 331267200, 11738697600, 464539452672, 20302660659456, 971106358760448, 50452643588275200, 2829000818124208128, 170271405502300207104, 10948525752699316371456, 748994717201835804033024, 54315931193865932254543872

Offset: 0

Author

Ilya Gutkovskiy, Mar 02 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A047053, A210246, A227917, A326324, A352069.

Programs

Mathematica

nmax = 18; CoefficientList[Series[1/(1 + Log[1 - 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! (-4)^(n - k), {k, 0, n}], {n, 0, 18}]

PARI

my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-4*x)/4))) \\ Michel Marcus, Mar 02 2022

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * (-4)^(n-k).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * 4^(k-1) * a(n-k).

a(n) ~ n! * 4^(n+1) * exp(4*n) / (exp(4) - 1)^(n+1). - Vaclav Kotesovec, Mar 03 2022