A177775 G.f. A(x) satisfies: [x^n] A_{n}(x) = [x^n] A_{n-1}(x) for n>2 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x.

1, 1, -4, 39, -580, 11480, -285116, 8617217, -311138320, 13245849264, -657721045720, 37721447340698, -2476051190767536, 184449202720026868, -15472664808232769104, 1451318259607442040637, -151254398423642331357224

Offset

1,3

Links

Table of n, a(n) for n=1..17.

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, -4,. 39,.. -580,. 11480,. -285116,.. 8617217,. -311138320,...];
[1, 2,(-6), 59,.. -898,. 18228,. -463816,. 14330618,. -527519702,...];
[1, 3,(-6),(66), -1048,. 21932,. -572180,. 18055088,. -676555682,...];
[1, 4, -4, (66),(-1100), 23750,. -634548,. 20415192,. -777438522,...];
[1, 5,. 0,. 65, (-1100),(24430), -666940,. 21835125,. -843666770,...];
[1, 6,. 6,. 69,. -1070, (24430),(-679756), 22603642,. -884811200,...];
[1, 7, 14,. 84,. -1008,. 24038, (-679756),(22919008), -907726332,...];
[1, 8, 24, 116,.. -888,. 23492,. -671320, (22919008),(-917372412),...];
[1, 9, 36, 171,.. -660,. 23100,. -656988,. 22701057, (-917372412),...]; ...
where the above coefficients in parenthesis illustrate the property
that the coefficients of x^n in A_{n}(x) and in A_{n-1}(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-1, G=subst(G, x, F)); H=subst(G, x, F); if(n<1, 0, if(n<3, 1, polcoeff(G-H, n)))}

Crossrefs

Cf. A177774, A177776.

Sequence in context: A319177 A323323 A300188 * A364981 A192935 A365010

Adjacent sequences: A177772 A177773 A177774 * A177776 A177777 A177778

Keyword

sign

Author

Paul D. Hanna, May 13 2010

Status

approved