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 A171212 G.f.: A(x) = x + x*A(A(2x)). 3
 1, 2, 16, 320, 12928, 985088, 140861440, 38451150848, 20403322617856, 21307854867660800, 44110759073910095872, 181739941085108158595072, 1493546441998961207249207296, 24512116566896662943648857456640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS More generally, if F(x) = x + x*F(F(qx)), then F(x) = x + x*F(qx) + x*F(qx)*F(qF(qx) + x*F(qx)*F(qF(qx))*F(qF(qF(qx))) +... with a simple solution at q=1/2: F(x) = x/(1-x/2) satisfies: F(x) = x + x*F(F(x/2)). LINKS Table of n, a(n) for n=0..13. EXAMPLE G.f.: A(x) = x + 2*x^2 + 16*x^3 + 320*x^4 + 12928*x^5 +... A(A(x)) = x + 4*x^2 + 40*x^3 + 808*x^4 + 30784*x^5 + 2200960*x^6 +...+ a(n)*x^n/2^(n-1) +... As a formal series involving products of iterations of the g.f., A(x) = x + x*A(2x) + x*A(2x)*A(2A(2x) + x*A(2x)*A(2A(2x))*A(2A(2A(2x))) +... which, upon replacing x with A(2x), yields: A(A(2x)) = A(2x) + A(2x)*A(2A(2x)) + A(2x)*A(2A(2x))*A(2A(2A(2x))) +... thus A(x) = x + x*A(A(2x)). PROG (PARI) {a(n, q=2)=local(A=x+x^2); for(i=1, n, A=x+x*subst(A, x, subst(A, x, q*x+O(x^n)))); polcoeff(A, n)} CROSSREFS Cf. A171213 (q=3), A171214 (q=1/3). Sequence in context: A282787 A137729 A278589 * A282392 A336522 A294039 Adjacent sequences: A171209 A171210 A171211 * A171213 A171214 A171215 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 08 2009 STATUS approved

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Last modified September 30 06:20 EDT 2023. Contains 365781 sequences. (Running on oeis4.)