A307084 Expansion of 1/(1 - 1^1*x/(1 - 2^2*x/(1 - 3^3*x/(1 - 4^4*x/(1 - 5^5*x/(1 - ...)))))), a continued fraction.

1, 1, 5, 133, 31769, 95375641, 4353388262525, 3536446917781244413, 58773633134246903294470769, 22612364832863674279489837434733681, 224919094724957152626614652086970769074005045, 63900685361274641827300282511815586348785532532913331893

Offset: 0

Author

Ilya Gutkovskiy, Mar 23 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..37

Crossrefs

Cf. A000312, A002109, A285380.

Programs

Mathematica

nmax = 11; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^k x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)^(n-i+1)*x/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 15 2021

Formula

a(n) ~ A002109(n). - Vaclav Kotesovec, Apr 15 2021