

A119817


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


5



1, 1, 2, 8, 40, 210, 1032, 4074, 9084, 1485, 139344, 1178057, 97107644, 533077818, 43465435335, 997494915376, 35039558716800, 1885975569825115, 36684866143759995, 4946226556607087316, 24828007395162323458, 18213320246807011794109
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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 nth 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, n1, 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((n1polcoeff(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



