A295072 Expansion of 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^(k*(k+1)*(k+2)/6)/(1 - ...))))))), a continued fraction.

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 51, 71, 98, 135, 188, 262, 364, 504, 699, 971, 1350, 1874, 2600, 3608, 5011, 6959, 9661, 13409, 18615, 25846, 35887, 49821, 69163, 96018, 133310, 185082, 256951, 356722, 495245, 687568, 954575, 1325251, 1839865, 2554325, 3546245, 4923342

Offset

0,6

Links

Table of n, a(n) for n=0..50.

Formula

G.f.: 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^A000292(k)/(1 - ...))))))), a continued fraction.

a(n) ~ c * d^n, where d = 1.388323040709674097023351236945145477752521994116275726548400298175286... and c = 0.369600335108282885310522776855743258910315692223280044555536918225... - Vaclav Kotesovec, Sep 18 2021

Mathematica

nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (k + 2)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000292, A206740, A285484, A295073.

Sequence in context: A352043 A087221 A352041 * A206739 A107586 A206737

Adjacent sequences: A295069 A295070 A295071 * A295073 A295074 A295075

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2017

Status

approved