A291274 a(n) = [x^n] 1/(1 - n*x/(1 - n*x^2/(1 - n*x^3/(1 - n*x^4/(1 - n*x^5/(1 - ...)))))), a continued fraction.

1, 1, 4, 36, 384, 5125, 81864, 1519833, 32219136, 768352149, 20367510000, 594270942705, 18929706034176, 653744865197242, 24333393186194848, 971177936039212500, 41376191798281502720, 1874320475909920820607, 89961819584112859211712, 4560744533588836253021837

Offset: 0

Author

Ilya Gutkovskiy, Aug 22 2017

Keywords

• nonn

Links

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

Crossrefs

Main diagonal of A286933.

Programs

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-n x^i, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 19}]

Formula

a(n) = A286933(n,n).

a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Aug 26 2017