A192209 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n^2)/(1 - x*A(x)^n)^n.

1, 1, 3, 13, 70, 431, 2904, 20884, 157881, 1242470, 10111281, 84700640, 727952319, 6403738619, 57563742289, 528125896942, 4941448428666, 47128664659641, 458055597979709, 4536505547203889, 45785021320327540, 470972703324515813

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 70*x^4 + 431*x^5 + 2904*x^6 +...
which satisfies:
A(x) = 1 + x*A(x)/(1-x*A(x)) + x^2*A(x)^4/(1-x*A(x)^2)^2 + x^3*A(x)^9/(1-x*A(x)^3)^3 +...

Prog

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

Crossrefs

Sequence in context: A119906 A059726 A274379 * A154677 A121586 A024337

Adjacent sequences: A192206 A192207 A192208 * A192210 A192211 A192212

Keyword

nonn

Author

Paul D. Hanna, Jun 25 2011

Status

approved