A307084 - OEIS

%I #16 Apr 15 2021 23:42:59

%S 1,1,5,133,31769,95375641,4353388262525,3536446917781244413,

%T 58773633134246903294470769,22612364832863674279489837434733681,

%U 224919094724957152626614652086970769074005045,63900685361274641827300282511815586348785532532913331893

%N 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.

%H Seiichi Manyama, <a href="/A307084/b307084.txt">Table of n, a(n) for n = 0..37</a>

%F a(n) ~ A002109(n). - _Vaclav Kotesovec_, Apr 15 2021

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

%o (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

%Y Cf. A000312, A002109, A285380.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 23 2019