0,3

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

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

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

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

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

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

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

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

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

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

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

(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)}

Cf. A107589 (variant).

Sequence in context: A103370 A094149 A117107 this_sequence A128326 A014333 A027710

Adjacent sequences: A159606 A159607 A159608 this_sequence A159610 A159611 A159612

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2009