Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
_Paul D. Hanna (pauldhanna(AT)juno.com), _, May 16 2009
G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(2^n).
1, 1, 3, 12, 57, 304, 1778, 11329, 79293, 626614, 5911340, 72622218, 1271963335, 33126504453, 1266054182987, 69124699233986, 5301840148829273, 566953161970598904, 84240794164243627206, 17363983133374688843928
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).
nonn
Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2009
approved