A306037 Expansion of e.g.f. 1/(1 + log(1 - log(1 + x))).

1, 1, 2, 7, 31, 178, 1200, 9588, 86592, 887086, 10035164, 125472246, 1705102394, 25175822644, 399387494956, 6801042408728, 123348694663480, 2379855020533664, 48569042602254128, 1047134236970183664, 23748242269316806752, 565834452464428045872, 14117321495269290091440

Offset

0,3

Links

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A007840(k).

a(n) ~ n! * exp(-exp(-1)) / (exp(1 - exp(-1)) - 1)^(n+1). - Vaclav Kotesovec, Jul 01 2018

Example

1/(1 + log(1 - log(1 + x))) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 178*x^5/5! + 1200*x^6/6! + ...

Maple

a:=series(1/(1+log(1-log(1+x))), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 22; CoefficientList[Series[1/(1 + Log[1 - Log[1 + x]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[StirlingS1[n, k] Abs[StirlingS1[k, j]] j!, {j, 0, k}], {k, 0, n}], {n, 0, 22}]
a[0] = 1; a[n_] := a[n] = Sum[Sum[(j - 1)! StirlingS1[k, j], {j, 1, k}] a[n - k]/k!, {k, 1, n}]; Table[n! a[n], {n, 0, 22}]

Crossrefs

Cf. A007840, A089064, A305323, A305988.

Sequence in context: A352309 A059037 A245313 * A046907 A365561 A365563

Adjacent sequences: A306034 A306035 A306036 * A306038 A306039 A306040

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 17 2018

Status

approved