cp's OEIS Frontend

A119817 Integer a(n) produces the least nonnegative integer coefficient of x^n in the n-th iteration of g.f. A(x).

%I A119817 #5 Aug 27 2013 02:04:54
%S A119817 1,1,-2,8,-40,210,-1032,4074,-9084,-1485,-139344,-1178057,97107644,
%T A119817 533077818,-43465435335,-997494915376,35039558716800,1885975569825115,
%U A119817 -36684866143759995,-4946226556607087316,24828007395162323458,18213320246807011794109
%N A119817 Integer a(n) produces the least nonnegative integer coefficient of x^n in the n-th iteration of g.f. A(x).
%e A119817 The successive iterations of g.f. A(x) begin:
%e A119817 A(x) = (1)x + x^2 - 2x^3 + 8x^4 - 40x^5 + 210x^6 - 1032x^7 + 4074x^8+..
%e A119817 A(A(x)) = x + (2)x^2 - 2x^3 + 7x^4 - 30x^5 + 118x^6 -268x^7 -1430x^8+..
%e A119817 A(A(A(x))) = x + 3x^2 + (0)x^3 + 3x^4 -12x^5 +18x^6 +240x^7 -3119x^8+..
%e A119817 A(A(A(A(x)))) = x + 4x^2 + 4x^3 + (2)x^4 - 4x^5 - 18x^6 + 276x^7+...
%e A119817 A(A(A(A(A(x))))) = x + 5x^2 + 10x^3 + 10x^4 +(0)x^5 -20*x^6 +128*x^7+..
%e A119817 A(A(A(A(A(A(x)))))) = x + 6x^2 + 18x^3 +33x^4 +30x^5 +(0)x^6 -24x^7+..
%e A119817 Coefficients [x^n] of n-th iteration of A(x) forms A119818:
%e A119817 [1,2,0,2,0,0,0,0,0,0,0,10,0,0,7,12,0,6,0,9,2,11,0,8,10,13,18,18,...].
%o A119817 (PARI) {a(n)=local(F=x+x^2+sum(k=3,n-1,a(k)*x^k),G=x+x*O(x^n)); if(n<1,0,if(n<=2,1, for(k=1,n,G=subst(F,x,G)); return((n-1-polcoeff(G,n,x)) )))}
%Y A119817 Cf. A119818, A119815, A112317.
%K A119817 sign
%O A119817 1,3
%A A119817 _Paul D. Hanna_, May 31 2006