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 A221585 G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) / (1 + x*A(x)^n)^n. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A151073 A063688 A245378 * A083862 A205543 A137590 Adjacent sequences:  A221582 A221583 A221584 * A221586 A221587 A221588 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 20 2013 STATUS approved

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Last modified July 22 02:20 EDT 2019. Contains 325210 sequences. (Running on oeis4.)