A187119 G.f. A(x) satisfies: [x^(m+2)] A(F^m(x)) = 0 for m>0 where F^m(x) denotes the m-th iteration of F(x) = x+x^2 with F^0(x)=x.

1, -2, 4, -12, 36, -140, 519, -2632, 11776, -82020, 426990, -4149112, 22719260, -309921456, 1487214652, -31477804596, 82495148888, -4227929653508, -7155535440434, -767565126075852, -6245080462329816, -194907866415800464

Offset

2,2

Links

Table of n, a(n) for n=2..23.

Example

G.f.: A(x) = x^2 - 2*x^3 + 4*x^4 - 12*x^5 + 36*x^6 - 140*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, -2, 4, -12, 36, -140, 519, -2632, 11776, ...];
[1, 0, -1, -2, -2, -28, -37, -760, -1752, -34632, ...];
[1, 2, 0, -6, -18, -64, -284, -1694, -10640, -82576, ...];
[1, 4, 7, 0, -46, -232, -1062, -5700, -36354, -268212, ...];
[1, 6, 20, 40, 0, -480, -3369, -19988, -126200, -904820, ...];
[1, 8, 39, 138, 326, 0, -6309, -56820, -417184, -3091852, ...];
[1, 10, 64, 318, 1258, 3492, 0, -100082, -1100188, -9660560, ...];
[1, 12, 95, 604, 3242, 14476, 46558, 0, -1859518, -24135624, ...];
[1, 14, 132, 1020, 6844, 40348, 202655, 744320, 0, -39597444, ...];
[1, 16, 175, 1590, 12750, 92140, 598083, 3354848, 13889080, 0, ...]; ...
in which the main diagonal equals all zeros after the initial '1';
the lower triangular portion of the above table forms triangle A187115.

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]); if(n<2, 0, for(i=1, n-1, A=concat(A, 0); A[#A]=-Vec(subst(x^2*Ser(A), x, ITERATE(x+x^2, i, #A)))[#A]); A[n-1])}

Crossrefs

Cf. A187009, A187124, A187115, A135082, A187116, A187117, A187118.

Sequence in context: A081443 A086647 A268600 * A062161 A195733 A046993

Adjacent sequences: A187116 A187117 A187118 * A187120 A187121 A187122

Keyword

sign

Author

Paul D. Hanna, Mar 08 2011

Status

approved