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 A214765 G.f. satisfies: A(x) = 1/A(-x*A(x)^5). 8
 1, 2, 12, 84, 616, 4832, 42112, 410368, 4316800, 46899648, 512004480, 5554843904, 59657443584, 633013100288, 6639969848320, 69332566233088, 733169635126272, 8068863012833280, 95049764691595264, 1213724245095528448, 16619899465108049920, 238054738089559379968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare g.f. to: G(x) = 1/G(-x*G(x)^5) when G(x) = 1 + x*G(x)^3 (A001764). An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^5); for example, (*) is satisfied by G(x) = F(m*x) = 1 + m*x*F(m*x)^3 for all m, where F(x) is the g.f. of A001764. LINKS FORMULA The g.f. of this sequence is the limit of the recurrence: (*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^5))/2 starting at G_0(x) = 1+2*x. EXAMPLE G.f.: A(x) = 1 + 2*x + 12*x^2 + 84*x^3 + 616*x^4 + 4832*x^5 + 42112*x^6 +... A(x)^3 = 1 + 6*x + 48*x^2 + 404*x^3 + 3432*x^4 + 29808*x^5 + 271056*x^6 +... A(x)^5 = 1 + 10*x + 100*x^2 + 980*x^3 + 9400*x^4 + 89632*x^5 + 866080*x^6 +... PROG (PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^5+x*O(x^n)))/2); polcoeff(A, n)} for(n=0, 31, print1(a(n), ", ")) CROSSREFS Cf. A214761, A214762, A214763, A214764, A214766, A214767, A214768, A214769. Sequence in context: A136278 A130464 A319326 * A006657 A105927 A316702 Adjacent sequences:  A214762 A214763 A214764 * A214766 A214767 A214768 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 29 2012 STATUS approved

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Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)