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O.g.f.: 1 / Sum_{n>=0} -n^n*(n-1)^(n-1) * exp(-n*(n-1)*x) * x^n / n!.
2

%I #8 Aug 22 2018 03:39:22

%S 1,1,3,19,223,4019,98071,3012595,111408735,4813926235,237893755847,

%T 13230156372931,817650834368367,55588558619887179,4122802071853330711,

%U 331247290236326404499,28660436738240190615167,2656810905539387715877787,262694577305483845458361767

%N O.g.f.: 1 / Sum_{n>=0} -n^n*(n-1)^(n-1) * exp(-n*(n-1)*x) * x^n / n!.

%H Vaclav Kotesovec, <a href="/A217906/b217906.txt">Table of n, a(n) for n = 0..300</a>

%F Convolution inverse of A217905.

%F a(n) ~ 2^(2*n - 2) * n^(n - 3/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^(n - 1/2) * (2-c)^(n-1)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - _Vaclav Kotesovec_, Aug 22 2018

%e O.g.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 223*x^4 + 4019*x^5 + 98071*x^6 +...

%e where

%e A(x) = 1/(1 - 1^1*0^0*x*exp(-1*0*x) - 2^2*1^1*exp(-2*1*x)*x^2/2! - 3^3*2^2*exp(-3*2*x)*x^3/3! - 4^4*3^3*exp(-4*3*x)*x^4/4! - 5^5*4^4*exp(-5*4*x)*x^5/5! +...).

%e simplifies to a power series in x with integer coefficients.

%o (PARI) {a(n)=polcoeff(1/sum(m=0,n,-m^m*(m-1)^(m-1)*x^m*exp(-m*(m-1)*x+x*O(x^n))/m!),n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A217905.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 14 2012