A143500 G.f. satisfies: A(x) = 1 + x*A(x*A(x)^2).

1, 1, 1, 3, 10, 46, 244, 1481, 10020, 74400, 599573, 5200284, 48223360, 475557054, 4965035754, 54672110310, 632853655686, 7678552433184, 97404631390960, 1288861146261679, 17752479062092470, 254051633672160696

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..230

Formula

G.f. satisfies: G(x) = x/[1 + A(x)*G(x)]^2 = x/A(G(x))^2 where G(x*A(x)^2) = x.

Example

G.f. A(x) = 1 + x + x^2 + 3*x^3 + 10*x^4 + 46*x^5 + 244*x^6 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 8*x^3 + 27*x^4 + 118*x^5 + 609*x^6 +...
A(x*A(x)^2) = 1 + x + 3*x^2 + 10*x^3 + 46*x^4 + 244*x^5 +...
If G(x*A(x)^2) = x then
G(x) = x - 2*x^2 + 5*x^3 - 18*x^4 + 68*x^5 - 300*x^6 + 1283*x^7 -+...
A(G(x)) = 1 + A(x)*G(x) = (x/G(x))^(1/2) where
A(x)*G(x) = x - x^2 + 4*x^3 - 12*x^4 + 59*x^5 - 209*x^6 + 1199*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^2)); polcoeff(A, n)}

Crossrefs

Cf. A143501.

Sequence in context: A355050 A371549 A074508 * A058112 A345132 A020008

Adjacent sequences: A143497 A143498 A143499 * A143501 A143502 A143503

Keyword

nonn

Author

Paul D. Hanna, Aug 20 2008

Status

approved