A291653 - OEIS

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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

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

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: A370624 A286191 A033887 * A183804 A117376 A264037

Adjacent sequences: A291650 A291651 A291652 * A291654 A291655 A291656

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 28 2017

STATUS

approved