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%I #7 Mar 30 2012 18:37:33
%S 1,2,22,980,161638,100318460,240313495420,2251316821283048,
%T 83005840299778004614,12089092134684999622076396,
%U 6972054121242613685463168904468,15950722005044706228925521886595357720,144954811888851643278920459489891540357638876
%N G.f.: [ Sum_{n>=0} (n+1) * 2^(n^2) * x^n ]^(1/2).
%C Equals the self-convolution square-root of A197927 (with offset).
%F a(n) = (n+1)*2^(n^2-1) - Sum_{k=1..n-1} a(n-k)*a(k)/2 for n>0 with a(0)=1.
%e G.f.: A(x) = 1 + 2*x + 22*x^2 + 980*x^3 + 161638*x^4 + 100318460*x^5 +...
%e where
%e A(x)^2 = 1 + 2*2*x + 3*2^4*x^2 + 4*2^9*x^3 + 5*2^16*x^4 + 6*2^25*x^5 +...
%e more explicitly,
%e A(x)^2 = 1 + 4*x + 48*x^2 + 2048*x^3 + 327680*x^4 + 201326592*x^5 +...+ A197927(n+1)*x^n +...
%o (PARI) {a(n)=polcoeff(sum(m=0,n,(m+1)*2^(m^2)*x^m+x*O(x^n))^(1/2),n)}
%o (PARI) {a(n)=if(n==0,1,(n+1)*2^(n^2-1)-sum(k=1,n-1,a(n-k)*a(k)/2))}
%Y Cf. A197927, A202942.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 26 2011
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