login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

G.f.: A(x) = exp( Sum_{n>=1} A(2^(n^2)*x^n)*x^n/n ).
1

%I #2 Mar 30 2012 18:37:23

%S 1,1,3,15,145,2489,83021,5402565,697174827,179186086779,

%T 91923934089991,94222398574777359,193061880430280639843,

%U 790974713509247761511635,6480456214858268755580705051,106182276664343738404944887223883

%N G.f.: A(x) = exp( Sum_{n>=1} A(2^(n^2)*x^n)*x^n/n ).

%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 145*x^4 + 2489*x^5 +...

%e The logarithm of the g.f. equals the series:

%e log(A(x)) = A(2*x)*x + A(2^4*x^2)*x^2/2 + A(2^9*x^3)*x^3/3 + A(2^16*x^4)*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,subst(A,x,2^(m^2)*x^m+x*O(x^n))*x^m/m)));polcoeff(A,n)}

%Y Cf. A181536.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 30 2010