A153304 G.f. satisfies: A(x) = x + 2*A(x)^2 + 3*A(x)*A(A(x))^2 + 4*A(x)*A(A(x))*A(A(A(x)))^2 +...

1, 2, 11, 86, 818, 8870, 105965, 1366392, 18765702, 271970994, 4131937389, 65478068666, 1078175171377, 18392088785962, 324248141334314, 5896276936120944, 110414710776883484, 2126330263151116868

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: A(x) = x/(1 - 2*A(A(x)) + A(A(x))*A(A(A(x))) ).

G.f.: A(x) = Series_Reversion[x*(1 - 2*A(x) + A(x)*A(A(x)) )].

Example

G.f.: A(x) = x + 2*x^2 + 11*x^3 + 86*x^4 + 818*x^5 + 8870*x^6 +...
A(A(x)) = x + 4*x^2 + 30*x^3 + 290*x^4 + 3251*x^5 + 40348*x^6 +...
A(A(A(x))) = x + 6*x^2 + 57*x^3 + 660*x^4 + 8603*x^5 + 121792*x^6 +...
A(x)^2 = x^2 + 4*x^3 + 26*x^4 + 216*x^5 + 2101*x^6 + 22904*x^7 +...
A(x)*A(A(x))^2 = x^3 + 10*x^4 + 103*x^5 + 1146*x^6 + 13704*x^7 +...
A(x)*A(A(x)) = x^2 + 6*x^3 + 49*x^4 + 480*x^5 + 5323*x^6 + 64762*x^7 +...
A(A(x))*A(A(A(x))) = x^2 + 10*x^3 + 111*x^4 + 1358*x^5 + 17944*x^6 +...
x/A(x) = 1 - 2*x - 7*x^2 - 50*x^3 - 469*x^4 - 5144*x^5 - 62752*x^6 -...
Series_Reversion(A(x)) = x - 2*x^2 - 3*x^3 - 16*x^4 - 123*x^5 - 1156*x^6 -...

Prog

(PARI) {a(n)=local(A=x+x*O(x)); for(i=1, n, A=serreverse(x*(1-2*A+A*subst(A, x, A)))); polcoeff(A, n)}

Crossrefs

Sequence in context: A074604 A135404 A370475 * A240998 A331876 A305537

Adjacent sequences: A153301 A153302 A153303 * A153305 A153306 A153307

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2009

Status

approved