OFFSET
0,4
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k)*A007325(k)*k!.
EXAMPLE
E.g.f.: A(x) = 1 - x + x^2/2! + 5*x^3/3! - 11*x^4/4! - 91*x^5/5! - 419*x^6/6! - 1555*x^7/7! + ...
MATHEMATICA
nmax = 22; CoefficientList[Series[1/(1 + ContinuedFractionK[(Exp[x] - 1)^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
b[n_] := b[n] = SeriesCoefficient[QPochhammer[x, x^5] QPochhammer[x^4, x^5]/(QPochhammer[x^2, x^5] QPochhammer[x^3, x^5]), {x, 0, n}]; a[n_] := a[n] = Sum[StirlingS2[n, k] b[k] k!, {k, 0, n}]; Table[a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 19 2018
STATUS
approved