A153305 G.f. satisfies: A(x) = x + 3*x*A(x) + 6*x*A(x)*A(A(x)) + 10*x*A(x)*A(A(x))*A(A(A(x))) +...

1, 3, 15, 109, 1008, 10983, 135097, 1828425, 26777775, 419530384, 6973851684, 122248585620, 2249238083514, 43274933036838, 868047525689328, 18108325893968859, 392039367345646323, 8792515088387598651

Offset

0,2

Links

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

Formula

x = A(x) - 3*x*A(A(x)) + 3*x*A(x)*A(A(A(x))) - x*A(x)*A(A(x))*A(A(A(A(x)))).

A(x) = x*(1 + 3*A(A(x)))/(1 + 3*x*A(A(A(x))) - x*A(A(x))*A(A(A(A(x))))).

A(x) = Series_Reversion[x/(1 + 3*A(x) - 3*x*A(A(x)) + x*A(x)*A(A(A(x))))].

Example

G.f.: A(x) = x + 3*x^2 + 15*x^3 + 109*x^4 + 1008*x^5 + 10983*x^6 +...
A(A(x)) = x + 6*x^2 + 48*x^3 + 470*x^4 + 5328*x^5 + 67557*x^6 +...
A(A(A(x))) = x + 9*x^2 + 99*x^3 + 1245*x^4 + 17280*x^5 + 259362*x^6 +...
A(A(A(A(x))) = x + 12*x^2 + 168*x^3 + 2596*x^4 + 43128*x^5 + 759306*x^6 +...
A(A(A(A(A(x)))) = x + 15*x^2 + 255*x^3 + 4685*x^4 + 91080*x^5 +...

Prog

(PARI) {a(n)=local(A=x+x*O(x), B, C); for(i=1, n, B=subst(A, x, A); C=subst(A, x, B); A=serreverse(x/(1+3*A-3*x*B+x*A*C))); polcoeff(A, n)}

Crossrefs

Cf. A119736.

Sequence in context: A090351 A136221 A366180 * A380080 A110328 A217061

Adjacent sequences: A153302 A153303 A153304 * A153306 A153307 A153308

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2009

Status

approved