A143501 G.f. satisfies: A(x) = 1 + x*A(x*A(x)^3).

1, 1, 1, 4, 16, 92, 616, 4729, 40776, 388057, 4028230, 45207583, 544680014, 7004865885, 95694153485, 1382946630490, 21067128029388, 337224872043659, 5656357906530796, 99168643108816180, 1813250965008114981

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

G.f. satisfies: G(x) = x/[1 + A(x)*G(x)]^3 = x/A(G(x))^3 where G(x*A(x)^3) = x.

Example

G.f. A(x) = 1 + x + x^2 + 4*x^3 + 16*x^4 + 92*x^5 + 616*x^6 + 4729*x^7 +...
A(x)^3 = 1 + 3*x + 6*x^2 + 19*x^3 + 78*x^4 + 411*x^5 + 2617*x^6 +...
A(x*A(x)^3) = 1 + x + 4*x^2 + 16*x^3 + 92*x^4 + 616*x^5 + 4729*x^6 +...
If G(x*A(x)^3) = x then
G(x) = x - 3*x^2 + 12*x^3 - 64*x^4 + 372*x^5 - 2385*x^6 + 15675*x^7 -+...
A(G(x)) = 1 + A(x)*G(x) = (x/G(x))^(1/3) where
A(x)*G(x) = x - 2*x^2 + 10*x^3 - 51*x^4 + 324*x^5 - 1985*x^6 + 13938*x^7 -...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, x*A^3)); polcoeff(A, n)}

Crossrefs

Cf. A143500.

Sequence in context: A009568 A139155 A003762 * A111291 A050913 A096243

Adjacent sequences: A143498 A143499 A143500 * A143502 A143503 A143504

Keyword

nonn

Author

Paul D. Hanna, Aug 20 2008

Status

approved