A177774 G.f. A(x) satisfies: [x^n] A_{n-1}(x) = [x^n] A_{n-2}(x) for n>2 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x.

1, 1, -2, 12, -120, 1684, -31120, 730167, -21231238, 750298888, -31687276404, 1575667784824, -91052587870552, 6045175643449008, -456560323906523200, 38886167319641201692, -3706800668529432678016, 392824268201002386964776

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

G.f.: A(x) = x + x^2 - 4*x^3 + 39*x^4 - 580*x^5 + 11480*x^6 +...
Coefficients in the initial iterations of A(x) begin:
[1, 1,(-2),. 12,. -120,. 1684,. -31120,.. 730167,. -21231238,...];
[1, 2,(-2), (15), -166,. 2482,. -48156,. 1173206,. -35125518,...];
[1, 3,. 0,. (15),(-180), 2832,. -57240,. 1438754,. -44147898,...];
[1, 4,. 4,.. 18, (-180),(2950), -61708,. 1591568,. -49868346,...];
[1, 5, 10,.. 30,. -160, (2950),(-63432), 1671151,. -53317312,...];
[1, 6, 18,.. 57,.. -90,. 2964, (-63432),(1702414), -55189776,...];
[1, 7, 28,. 105,... 84,. 3262,. -61768, (1702414),(-55964444),...];
[1, 8, 40,. 180,.. 440,. 4372,. -56712,. 1688208, (-55964444),...]; ...
where the above coefficients in parenthesis illustrate the property
that the coefficients of x^n in A_{n-1}(x) and in A_{n-2}(x) are equal.

Prog

(PARI) {a(n)=local(F=x+x^2+sum(m=3, n-1, a(m)*x^m)+x*O(x^n), G=x, H); for(i=1, n-2, G=subst(G, x, F)); H=subst(G, x, F); if(n<1, 0, if(n<3, 1, polcoeff(G-H, n)))}

Crossrefs

Cf. A177775, A177776.

Sequence in context: A226759 A303557 A131815 * A047793 A048800 A251185

Adjacent sequences: A177771 A177772 A177773 * A177775 A177776 A177777

Keyword

sign

Author

Paul D. Hanna, May 13 2010

Status

approved