A192315 G.f. A(x) satisfies: A(x)^2 = Sum_{n>=0} x^n*A(x)^(2^n).

1, 1, 2, 6, 23, 105, 556, 3409, 24664, 218686, 2499812, 38628853, 829097387, 24849303505, 1035428836952, 59712082983706, 4754866838971645, 522450200091413797, 79208256385834752898, 16575527137487435275695

Offset

0,3

Links

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

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(2^n-1).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 105*x^5 + 556*x^6 +...
which satisfies:
A(x)^2 = A(x) + x*A(x)^2 + x^2*A(x)^4 + x^3*A(x)^8 + x^4*A(x)^16 +...
where:
A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 62*x^4 + 280*x^5 + 1450*x^6 + 8626*x^7 +...
A(x)^4 = 1 + 4*x + 14*x^2 + 52*x^3 + 213*x^4 + 968*x^5 + 4896*x^6 + 27836*x^7 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^(2^m-1))); polcoeff(A, n)}

Crossrefs

Sequence in context: A200406 A165489 A352367 * A325297 A288912 A193321

Adjacent sequences: A192312 A192313 A192314 * A192316 A192317 A192318

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2011

Status

approved