A159609 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

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

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.

Prog

(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)}

Crossrefs

Cf. A107589 (variant).

Sequence in context: A094149 A291695 A117107 * A128326 A323631 A014333

Adjacent sequences: A159606 A159607 A159608 * A159610 A159611 A159612

Keyword

nonn

Author

Paul D. Hanna, May 16 2009

Status

approved