OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..61
FORMULA
G.f.: 1/(1 - x/(1 - 2x/(1 - 5x/(1 - 14x/(1 - 42x/(1 -...)))))), by definition.
a(n) ~ c * A003046(n) ~ c * A^(3/2) * 2^(n^2+n-19/24) * exp(3*n/2-1/8) / (n^(3*n/2+15/8) * Pi^(n/2+1)), where A is the Glaisher-Kinkelin constant A074962 and c = 1/Product_{k>=1} (1 - 1/4^k) = 1/QPochhammer[1/4] = 1.452353642449597... - Vaclav Kotesovec, Aug 26 2017
MATHEMATICA
Table[SeriesCoefficient[Series[1/(1+ContinuedFractionK[-CatalanNumber[k]*x, 1, {k, 1, 50}]), {x, 0, 50}], n], {n, 1, 50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benedict W. J. Irwin, Feb 09 2016
EXTENSIONS
a(0) = 1 added by Peter Bala, Apr 17 2017
STATUS
approved