A305323 Expansion of e.g.f. 1/(1 + log(1 + log(1 - x))).

1, 1, 4, 25, 211, 2238, 28560, 425808, 7261200, 139367278, 2973006344, 69775267186, 1786673529746, 49565881948204, 1480900541242572, 47407364553205448, 1618838460981098680, 58734896900587841824, 2256402484187691207152, 91499934912942249975504, 3905739517580787866827872

Offset: 0

Author

Ilya Gutkovskiy, May 30 2018

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 25*x^3/3! + 211*x^4/4! + 2238*x^5/5! + 28560*x^6/6! + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..399

Crossrefs

Cf. A003713, A007840, A217033, A305988.

Programs

Maple

S:= series(1/(1+log(1+log(1-x))),x,31):
seq(coeff(S,x,n)*n!,n=0..30); # Robert Israel, May 31 2018

Mathematica

nmax = 20; CoefficientList[Series[1/(1 + Log[1 + Log[1 - x]]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Sum[(j - 1)! Abs[StirlingS1[k, j]], {j, 1, k}] a[n - k]/k!, {k, 1, n}]; Table[n! a[n], {n, 0, 20}]

PARI

x = 'x + O('x^30); Vec(serlaplace(1/(1 + log(1 + log(1 - x))))) \\ Michel Marcus, May 31 2018

Formula

a(n) ~ n! / (exp(2 - exp(-1)) * (1 - exp(exp(-1) - 1))^(n+1)). - Vaclav Kotesovec, May 31 2018

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A007840(k). - Seiichi Manyama, May 11 2023