%I
%S 1,4,24,416,34400,13561728,22961051392,160934805885952,
%T 4612329945733989888,537318814887463743641600,
%U 253532269357851227988228362240,483356648964255814869226601582346240
%N Selfconvolution of A155200.
%F G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2+1)*x^n/n ).
%F a(n) = (1/n)*Sum_{k=1..n} 2^(k^2+1)*a(nk), a(0) = 1.
%e G.f.: A(x) = 1 + 4*x + 24*x^2 + 416*x^3 + 34400*x^4 + 13561728*x^5 +...
%e A(x)^(1/2) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 + 6745436*x^5 +...
%e log(A(x)) = 2^2*x + 2^5*x^2/2 + 2^10*x^3/3 + 2^17*x^4/4 + 2^26*x^5/5 +...
%o (PARI) {a(n)=polcoeff(exp( 2*sum(k=1, n, 2^(k^2)*x^k/k)+x*O(x^n)), n)}
%o (PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, 2^(k^2+1)*a(nk)))}
%Y Cf. A155200.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 30 2009
