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 A177776 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. 2
 1, 1, -6, 80, -1570, 39914, -1242192, 45954240, -1986728358, 99266274404, -5684436494176, 370411466138116, -27283461238591012, 2257174498490657648, -208468812531599092816, 21371789110179099868480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..16. 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 Cf. A177774, A177775. Sequence in context: A275137 A167570 A337564 * A349528 A132616 A349657 Adjacent sequences: A177773 A177774 A177775 * A177777 A177778 A177779 KEYWORD sign AUTHOR Paul D. Hanna, May 13 2010 STATUS approved

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Last modified June 2 07:25 EDT 2023. Contains 363081 sequences. (Running on oeis4.)