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%I #9 Apr 13 2023 08:19:39
%S 1,1,2,6,23,110,630,4200,31990,274051,2608220,27304530,311820630,
%T 3857738170,51397726380,733698365400,11171708347799,180738402744866,
%U 3096027531044102,55980949167688884,1065496642477438890,21293801805033731190,445818117237227995260
%N Expansion of e.g.f. 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).
%H Paul D. Hanna, <a href="/A205802/b205802.txt">Table of n, a(n) for n = 0..400</a>
%F E.g.f.: 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 6*x^3/3! + 23*x^4/4! + 110*x^5/5! + ...
%e where
%e 1/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(sum(m=0, sqrtint(n+1), (-1)^m*x^(m^2)/(m^2)!+x*O(x^n))^(-1), n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A198891, A205800, A205801.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 31 2012
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