A217033 Expansion of e.g.f. 1/(1 - log(1 - log(1-x))).

1, 1, 2, 7, 33, 198, 1432, 12136, 117772, 1287718, 15658052, 209568126, 3061140398, 48454548452, 826155841924, 15094511153752, 294206836405288, 6093273074402848, 133628182522968752, 3093469935389714928, 75384936371166307872, 1928960833317580172688

Offset: 0

Author

Paul D. Hanna, Sep 24 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 33*x^4/4! + 198*x^5/5! +...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A089064, A305323.

Programs

Mathematica

CoefficientList[Series[1/(1-Log[1-Log[1-x]]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 12 2013 *)

PARI

{a(n)=n!*polcoeff(1/(1-log(1-log(1-x +x*O(x^n)))),n)}
for(n=0,25,print1(a(n),", "))

Formula

a(n) ~ n! * exp(2-exp(1))/(1-exp(1-exp(1)))^(n+1). - Vaclav Kotesovec, Feb 12 2013

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A006252(k). - Seiichi Manyama, May 11 2023