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
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
Programs
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Mathematica
nmax = 22; CoefficientList[Series[1/(1 + ContinuedFractionK[-Log[1 + x]^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(n) = Sum_{k=0..n} Stirling1(n,k)*A005169(k)*k!.