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%I #5 Oct 09 2014 12:54:59
%S 1,1,3,6,19,56,186,615,2127,7467,26720,96801,354901,1313293,4900266,
%T 18413166,69620351,264673536,1011100541,3879382837,14942671683,
%U 57760251344,223988614094,871159201568,3397330833310,13281696243924,52042973504510,204357290336561,804029764090404
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * (A(x) + x^n)^n.
%F G.f. satisfies: A(x) = Sum_{n>=1} x^(n*(n-1)) / (1 - A(x)*x^n)^n.
%e G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 19*x^4 + 56*x^5 + 186*x^6 +...
%e where the g.f. satisfies following series identity:
%e A(x) = 1 + x*(A(x)+x) + x^2*(A(x)+x^2)^2 + x^3*(A(x)+x^3)^3 + x^4*(A(x)+x^4)^4 + x^5*(A(x)+x^5)^5 + x^6*(A(x)+x^6)^6 +...
%e A(x) = 1/(1-A(x)*x) + x^2/(1-A(x)*x^2)^2 + x^6/(1-A(x)*x^3)^3 + x^12/(1-A(x)*x^4)^4 + x^20/(1-A(x)*x^5)^5 + x^30/(1-A(x)*x^6)^6 + x^42/(1-A(x)*x^7)^7 +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, x^k * (A + x^k +x*O(x^n))^k)); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=1, sqrtint(2*n+1), x^(k*(k-1)) / (1 - A*x^k +x*O(x^n))^k )); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 09 2014
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