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

1, 1, -2, 8, -40, 210, -1032, 4074, -9084, -1485, -139344, -1178057, 97107644, 533077818, -43465435335, -997494915376, 35039558716800, 1885975569825115, -36684866143759995, -4946226556607087316, 24828007395162323458, 18213320246807011794109

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Example

The successive iterations of g.f. A(x) begin:
A(x) = (1)x + x^2 - 2x^3 + 8x^4 - 40x^5 + 210x^6 - 1032x^7 + 4074x^8+..
A(A(x)) = x + (2)x^2 - 2x^3 + 7x^4 - 30x^5 + 118x^6 -268x^7 -1430x^8+..
A(A(A(x))) = x + 3x^2 + (0)x^3 + 3x^4 -12x^5 +18x^6 +240x^7 -3119x^8+..
A(A(A(A(x)))) = x + 4x^2 + 4x^3 + (2)x^4 - 4x^5 - 18x^6 + 276x^7+...
A(A(A(A(A(x))))) = x + 5x^2 + 10x^3 + 10x^4 +(0)x^5 -20*x^6 +128*x^7+..
A(A(A(A(A(A(x)))))) = x + 6x^2 + 18x^3 +33x^4 +30x^5 +(0)x^6 -24x^7+..
Coefficients [x^n] of n-th iteration of A(x) forms A119818:
[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,...].

Prog

(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)) )))}

Crossrefs

Cf. A119818, A119815, A112317.

Sequence in context: A003305 A076625 A139415 * A025570 A227081 A113449

Adjacent sequences: A119814 A119815 A119816 * A119818 A119819 A119820

Keyword

sign

Author

Paul D. Hanna, May 31 2006

Status

approved