A199544 - OEIS

%I #7 Mar 30 2012 18:37:32

%S 1,3,23,271,3876,61809,1057324,18999550,354126904,6790260312,

%T 133193201306,2661966127599,54046089492190,1112240570177203,

%U 23161201079072759,487383250552812705,10353102122586909350,221819714961583800336,4790442570608936302923

%N G.f.: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) * (1 - A(x)^(2*n+1))/(1 - A(x)).

%e G.f.: A(x) = 1 + 3*x + 23*x^2 + 271*x^3 + 3876*x^4 + 61809*x^5 +...

%e where the g.f. A = A(x) satisfies the equivalent expressions:

%e A = 1 + x*A*(1-A^3)/(1-A) + x^2*A^4*(1-A^5)/(1-A) + x^3*A^9*(1-A^7)/(1-A) + x^4*A^16*(1-A^9)/(1-A) + x^5*A^25*(1-A^11)/(1-A) +...

%e A = 1 + x*(A + A^2 + A^3) + x^2*(A^4 + A^5 + A^6 + A^7 + A^8) + x^3*(A^9 + A^10 + A^11 + A^12 + A^13 + A^14 + A^15) +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,x^m*A^(m^2)*sum(k=0,2*m,A^k)+x*O(x^n)));polcoeff(A,n)}

%Y Cf. A199543, A199409.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 07 2011