OFFSET
1,3
EXAMPLE
G.f.: A(x) = x + x^2 - 6*x^3 + 80*x^4 - 1570*x^5 + 39914*x^6 +...
Coefficients in the initial iterations of A(x) begin:
[1, 1,. -6,.. 80,. -1570,.. 39914,. -1242192,.. 45954240,...];
[1, 2, -10,. 131,. -2582,.. 66364,. -2092772,.. 78479586,...];
[1, 3,(-12), 159,. -3182,.. 83072,. -2659272,. 101127541,...];
[1, 4,(-12),(170), -3492,.. 92922,. -3022460,. 116545332,...];
[1, 5, -10, (170),(-3610),. 98080,. -3241848,. 126687816,...];
[1, 6,. -6,. 165, (-3610),(100114), -3360480,. 132988310,...];
[1, 7,.. 0,. 161,. -3542, (100114),(-3409000), 136493385,...];
[1, 8,.. 8,. 164,. -3432,.. 98812, (-3409000),(137966664),...];
[1, 9,. 18,. 180,. -3282,.. 96702,. -3375648, (137966664),...]; ...
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, G=subst(G, x, F)); H=subst(G, x, F); if(n<1, 0, if(n<3, 1, polcoeff(G-H, n)))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 13 2010
STATUS
approved