A187009 G.f. A(x) satisfies: [x^(n+1)] A(F^n(x)) = 0 for n>0 where F^n(x) denotes the n-th iteration of F(x) = x+x^2 with F^0(x)=x.

1, -1, 2, -6, 20, -80, 348, -1778, 9892, -64392, 449596, -3609782, 30152616, -284037468, 2694480888, -28592860322, 295151311376, -3440953545088, 37165311149276, -471576198145144, 5062381083026352, -71104461751595892

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Example

 G.f.: A(x) = x - x^2 + 2*x^3 - 6*x^4 + 20*x^5 - 80*x^6 + 348*x^7 +...
Let F^n(x) denote the n-th iteration of F(x) = x+x^2 with F^0(x)=x,
then the table of coefficients in A(F^n(x)), n>=0, begins:
[1, -1, 2, -6, 20, -80, 348, -1778, 9892, -64392, ...];
[1, 0, 0, -1, 2, -14, 44, -348, 1476, -14148, 73920, ...];
[1, 1, 0, -1, -2, -10, -24, -231, -654, -9276, -32456, ...];
[1, 2, 2, 0, -6, -26, -108, -570, -3216, -22622, -162596, ...];
[1, 3, 6, 8, 0, -54, -324, -1776, -10594, -71702, -540448, ...];
[1, 4, 12, 29, 50, 0, -616, -4846, -32686, -228926, -1749972, ...];
[1, 5, 20, 69, 202, 436, 0, -8629, -84140, -680298, -5508864, ...];
[1, 6, 30, 134, 538, 1880, 4912, 0, -143442, -1672428, -15821492, ...];
[1, 7, 42, 230, 1164, 5404, 22108, 68098, 0, -2762748, -37526484, ...];
[1, 8, 56, 363, 2210, 12646, 67092, 315784, 1122952, 0, -60534272, ..];
[1, 9, 72, 539, 3830, 25930, 166520, 997581, 5322126, 21488640, 0, ..]; ...
in which the main diagonal equals all zeros after the initial '1';
the lower triangular portion of the above table forms triangle A187005.

Prog

 (PARI) {ITERATE(F, n, p)=local(G=x); for(i=1, n, G=subst(F, x, G+x*O(x^p))); G}
{a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(subst(x*Ser(A), x, ITERATE(x+x^2, i, #A)))[#A]); A[n]}

Crossrefs

Cf. A187005, A135080, A122888, A135081, A187006, A187007, A187008.

Sequence in context: A150185 A354737 A357502 * A144168 A177482 A300011

Adjacent sequences: A187006 A187007 A187008 * A187010 A187011 A187012

Keyword

sign

Author

Paul D. Hanna, Mar 02 2011

Status

approved