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 A159609 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(2^n). 2

%I

%S 1,1,3,12,57,304,1778,11329,79293,626614,5911340,72622218,1271963335,

%T 33126504453,1266054182987,69124699233986,5301840148829273,

%U 566953161970598904,84240794164243627206,17363983133374688843928

%N G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(2^n).

%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 57*x^4 + 304*x^5 + 1778*x^6 +...

%e A(x) = 1 + x*A(x)^2 + x^2*A(x)^4 + x^3*A(x)^8 + x^4*A(x)^16 +...

%e Coefficients in A(x)^(2^n) begin:

%e A^(2^1): 1, 2, 7, 30, 147, 794, 4650, 29406, 202457, 1557116,...

%e A^(2^2): 1, 4, 18, 88, 463, 2596, 15434, 97348, 656887, 4848180,...

%e A^(2^3): 1, 8, 52, 320, 1954, 12064, 76048, 493112, 3319447,...

%e A^(2^4): 1, 16, 168, 1472, 11732, 88672, 650736, 4708208, 33976754,..

%e A^(2^5): 1, 32, 592, 8320, 98792, 1047360, 10247712, 94572768,...

%e A^(2^6): 1, 64, 2208, 54528, 1080528, 18268288, 273718592,...

%e A^(2^7): 1, 128, 8512, 391680, 14015904, 415639808, 10630692480,...

%e where antidiagonal sums of above coefficients = this sequence shift left.

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(2^j))); polcoeff(A, n)}

%Y Cf. A107589 (variant).

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 16 2009

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Last modified July 21 21:14 EDT 2019. Contains 325199 sequences. (Running on oeis4.)