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 A211828 G.f. satisfies: A(x) = x + x^2 * d/dx A(A(x)). 1
 1, 1, 4, 30, 324, 4480, 74544, 1438808, 31459536, 766573668, 20569553080, 602290243456, 19105119410064, 652635503205608, 23888307843434944, 932847459551529600, 38716407912891973504, 1702050349577155752784, 79018450946973490981176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..19. FORMULA G.f. satisfies: A(x) = x + x^2 * A'(x) * A'(A(x)). EXAMPLE G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 324*x^5 + 4480*x^6 + 74544*x^7 +... Related expansions: A'(x) = 1 + 2*x + 12*x^2 + 120*x^3 + 1620*x^4 + 26880*x^5 + 521808*x^6 +... A(A(x)) = x + 2*x^2 + 10*x^3 + 81*x^4 + 896*x^5 + 12424*x^6 + 205544*x^7 +... PROG (PARI) {a(n)=local(A=x+x^2+x*O(x^n)); for(i=1, n, A=x+x^2*deriv(subst(A, x, A))); polcoeff(A, n)} for(n=1, 21, print1(a(n), ", ")) CROSSREFS Cf. A211827. Sequence in context: A293191 A180623 A128329 * A277759 A006149 A207833 Adjacent sequences: A211825 A211826 A211827 * A211829 A211830 A211831 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 21 2012 STATUS approved

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Last modified September 23 04:08 EDT 2023. Contains 365532 sequences. (Running on oeis4.)