A291653 a(n) = [x^n] (1/(1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...)))))))^n, a continued fraction.

1, 1, 3, 13, 55, 236, 1035, 4593, 20551, 92578, 419338, 1907951, 8713555, 39921038, 183396671, 844515563, 3896933367, 18014916576, 83415684654, 386807933378, 1796024496430, 8349190182990, 38854827380075, 180997895984903, 843906670596499, 3938005827167461, 18390418912425940

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

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

Formula

a(n) = A291652(n,n).

a(n) ~ c * d^n / sqrt(n), where d = 4.760595370947474723688065553003203505424287110594102605580439495640678... and c = 0.22756527349964754363249384886359862025065238... - Vaclav Kotesovec, Apr 08 2018

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-x^i, 1, {i, 1, n}])^n, {x, 0, n}], {n, 0, 26}]

Crossrefs

Main diagonal of A291652.

Cf. A291274, A291651.

Sequence in context: A296045 A286191 A033887 * A183804 A117376 A264037

Adjacent sequences: A291650 A291651 A291652 * A291654 A291655 A291656

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 28 2017

Status

approved