A291651 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, -7, 15, -26, 15, 153, -1049, 4790, -18522, 64481, -206181, 606384, -1615121, 3715993, -6289929, 550850, 61250694, -382787092, 1726745790, -6691501530, 23413714107, -75179994017, 221304346963, -586004040651, 1318720868416, -2044320913276, -1137686341077, 28530838758784, -165361803129585

Offset: 0

Author

Ilya Gutkovskiy, Aug 28 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Crossrefs

Main diagonal of A286509.

Cf. A291335.

Programs

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[x^i, 1, {i, 1, n}])^n, {x, 0, n}], {n, 0, 30}]

Formula

a(n) = A286509(n,n).