A221585 G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) / (1 + x*A(x)^n)^n.

1, 1, 1, 3, 10, 39, 170, 788, 3885, 20060, 107989, 603762, 3496305, 20943217, 129663393, 829488918, 5483243950, 37460570247, 264551156875, 1931501448369, 14578396143512, 113720726834349, 916367532085433, 7622370642112803, 65390072935144713, 577947703151643232

Offset

0,4

Comments

Note that if G(x) = Sum_{n>=0} x^n*G(x)^(n^2)/(1 + x*G(x)^n)^(n+1), then G(x) = 1.

Note that if F(x) = Sum_{n>=0} x^n*F(x)^n / (1 + x*F(x))^n, then F(x) = 1/(1-x).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 170*x^6 + 788*x^7 +...
where
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 + x^4*A(x)^16/(1 + x*A(x)^4)^4 + x^5*A(x)^25/(1 + x*A(x)^5)^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*A^(m^2)/(1+x*subst(A, x, x+x*O(x^n))^m)^m)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A301928, A221546, A221586.

Sequence in context: A063688 A245378 A350915 * A083862 A205543 A137590

Adjacent sequences: A221582 A221583 A221584 * A221586 A221587 A221588

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2013

Status

approved