A228883 G.f. satisfies: x = A(x - A^2(x - A^3(x - A^4(x - A^5(x -...))))).

1, 1, 4, 22, 150, 1173, 10148, 94925, 945972, 9941558, 109382042, 1253180343, 14889508598, 182880186850, 2316222358948, 30188514546787, 404233232273788, 5553341502305868, 78182001588059148, 1126836634877469526, 16612944202665079800, 250345193073480290120

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..150

Example

G.f.: A(X) = x + x^2 + 4*x^3 + 22*x^4 + 150*x^5 + 1173*x^6 + 10148*x^7 +...
Let G(x) be the series reversion of A(x), then
B(x)^2 = x - G(x) = x^2 + 2*x^3 + 7*x^4 + 40*x^5 + 277*x^6 + 2200*x^7 + 19211*x^8 +...
B(x) = x + x^2 + 3*x^3 + 17*x^4 + 117*x^5 + 932*x^6 + 8178*x^7 + 77396*x^8 +...
C(x)^3 = x - G(B(x)) = x^3 + 3*x^4 + 15*x^5 + 88*x^6 + 618*x^7 + 4872*x^8 +...
C(x) = x + x^2 + 4*x^3 + 21*x^4 + 144*x^5 + 1131*x^6 + 9828*x^7 + 92275*x^8 +...
D(x)^4 = x - G(C(x)) = x^4 + 4*x^5 + 22*x^6 + 140*x^7 + 1005*x^8 + 7980*x^9 +...
D(x) = x + x^2 + 4*x^3 + 22*x^4 + 149*x^5 + 1166*x^6 + 10096*x^7 + 94517*x^8 +...
E(x)^5 = x - G(D(x)) = x^5 + 5*x^6 + 30*x^7 + 200*x^8 + 1475*x^9 + 11841*x^10 +...
E(x) = x + x^2 + 4*x^3 + 22*x^4 + 150*x^5 + 1172*x^6 + 10140*x^7 + 94862*x^8 +...
...

Prog

(PARI) {a(n)=local(A=x+x^2, G=x^(n+1)); for(i=1, n+1, A=serreverse(x-G+x^2*O(x^n)); G=x^(n+1)+x^2*O(x^n); for(k=0, n-1, G=subst(A^(n-k+1), x, x-G+x^2*O(x^n)))); polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A228862.

Sequence in context: A253095 A111529 A346764 * A307439 A189845 A039304

Adjacent sequences: A228880 A228881 A228882 * A228884 A228885 A228886

Keyword

nonn

Author

Paul D. Hanna, Sep 06 2013

Status

approved