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 A137984 G.f.: A(x) = 1/(1 - 2*x*[A_1(x)]^(1/2)); A_1(x) = 1/(1 - 4*x*[A_2(x)]^(1/4)); ...; where A_{n-1}(x) = 1/(1 - 2^n*x*[A_{n}(x)]^(1/2^n)) for n>=1 with A_0(x)=A(x). 1
 1, 2, 8, 44, 304, 2572, 26720, 347832, 5857280, 132320524, 4142751104, 183830444712, 11695392882688, 1070962802526776, 141154845280097280, 26736918028187247344, 7263732704774358982656, 2824813896305950802751372 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. EXAMPLE G.f.: A(x) = 1 + 2*x + 8*x^2 + 44*x^3 + 304*x^4 + 2572*x^5 +...; A_1(x) = 1 + 2*x + 10*x^2 + 72*x^3 + 670*x^4 + 7824*x^5 +...; A_2(x) = 1 + 2*x + 14*x^2 + 144*x^3 + 1934*x^4 + 32896*x^5 +...; A_3(x) = 1 + 2*x + 22*x^2 + 352*x^3 + 7262*x^4 + 188352*x^5 +...; A_4(x) = 1 + 2*x + 38*x^2 + 1024*x^3 + 34494*x^4 + 1425856*x^5 +...; A_5(x) = 1 + 2*x + 70*x^2 + 3392*x^3 + 198270*x^4 + 13714368*x^5 +...; ... where A(x) = 1/(1 - 2*x*[A_1(x)]^(1/2)); A_1(x) = 1/(1 - 4*x*[A_2(x)]^(1/4)); A_2(x) = 1/(1 - 8*x*[A_3(x)]^(1/8)); A_3(x) = 1/(1 - 16*x*[A_4(x)]^(1/16)); A_4(x) = 1/(1 - 32*x*[A_5(x)]^(1/32)); ... PROG (PARI) {a(n)=local(A=1+2^(n+1)*x+x*O(x^n)); for(i=0, n-1, A=1/(1-2^(n-i)*x*A^(1/2^(n-i))+x*O(x^n))); polcoeff(A, n)} CROSSREFS Sequence in context: A124467 A075792 A052897 * A191810 A172109 A005649 Adjacent sequences: A137981 A137982 A137983 * A137985 A137986 A137987 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 25 2008 STATUS approved

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Last modified February 24 14:03 EST 2024. Contains 370303 sequences. (Running on oeis4.)