A306038 Expansion of e.g.f. (1 + x)/(1 - log(1 + x)).

1, 2, 3, 5, 12, 34, 122, 482, 2328, 11640, 71952, 424368, 3312240, 21357504, 217045488, 1351338864, 19990187520, 89379824256, 2631270916224, 892036259712, 507945420198144, -3068802187635456, 142961233091051520, -1849617314640322560, 55640352746480440320

Offset: 0

Author

Ilya Gutkovskiy, Jun 17 2018

Keywords

• sign

Examples

			(1 + x)/(1 - log(1 + x)) = 1 + 2*x + 3*x^2/2! + 5*x^3/3! + 12*x^4/4! + 34*x^5/5! + 122*x^6/6! + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..452
• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000522, A006252, A059099, A089064.

Programs

Maple

S:= series((1+x)/(1-log(1+x)),x,51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Jun 19 2018

Mathematica

nmax = 24; CoefficientList[Series[(1 + x)/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
FullSimplify[Table[Sum[StirlingS1[n, k] E Gamma[1 + k, 1], {k, 0, n}], {n, 0, 24}]]

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000522(k).