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A306038 Expansion of e.g.f. (1 + x)/(1 - log(1 + x)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

FORMULA

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

EXAMPLE

(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! + ...

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}]]

CROSSREFS

Cf. A000522, A006252, A059099, A089064.

Sequence in context: A319912 A153987 A228905 * A008323 A000997 A266541

Adjacent sequences:  A306035 A306036 A306037 * A306039 A306040 A306041

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 17 2018

STATUS

approved

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Last modified July 8 19:01 EDT 2020. Contains 335524 sequences. (Running on oeis4.)