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 A205804 E.g.f.: -log( Sum_{n>=0} (-x)^(n^2) / (n^2)! ). 4

%I

%S 1,1,2,5,19,90,510,3395,25831,221140,2104310,22027170,251540795,

%T 3111928820,41460769350,591847005749,9011786683883,145794610986004,

%U 2497443795363566,45157627509568965,859494143391347310,17176870199851102510,359623890969235361700

%N E.g.f.: -log( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

%e E.g.f.: A(x) = x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 19*x^5/5! + 90*x^6/6! +...

%e where

%e exp(-A(x)) = 1 - x + x^4/4! - x^9/9! + x^16/16! - x^25/25! + x^36/36! +...

%o (PARI) {a(n)=n!*polcoeff(-log(sum(m=0, sqrtint(n+1), (-x)^(m^2)/(m^2)!+x*O(x^n))), n)}

%Y Cf. A205802, A205803.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jan 31 2012

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Last modified September 26 05:07 EDT 2021. Contains 347664 sequences. (Running on oeis4.)