A322342 - OEIS

A322342

Expansion of e.g.f. 1/(1 - log(1 + x)/(1 - log(1 + x)^2/(1 - log(1 + x)^3/(1 - ...)))), a continued fraction.

1, 1, 1, 8, 16, 224, 1328, 8280, 192960, 337992, 33969672, 11690832, 7909754400, -2553028752, 2357881048560, 3942533549568, 661635400722048, 13397372969553792, -107825500036658304, 22964754191590789632, -572404186520543904768, 31472786179436211417600, -886973046496642227294720

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

FORMULA

a(n) = Sum_{k=0..n} Stirling1(n,k)*A005169(k)*k!.

MATHEMATICA

nmax = 22; CoefficientList[Series[1/(1 + ContinuedFractionK[-Log[1 + x]^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A005169, A048594, A301921, A322470.