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A119815 Integer a(n) produces the least positive integer coefficient of x^n in the n-th iteration of g.f. A(x) where A(0)=0. 5
1, 1, -1, 1, 1, -11, 23, -20, 731, -4860, -91205, 138329, 24813133, 222203538, -11857627480, -340590475934, 7798573417057, 602467423292955, -4252676907049394, -1469602631093521547, -14928401886412967891, 4982240895059491727005, 167923794808862463264206 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

The iterated iterations of g.f. A(x) begin:

A(x) = (1)x + x^2 - x^3 + x^4 + x^5 - 11x^6 + 23x^7 - 20x^8 + 731x^9+..

A(A(x)) = x + (2)x^2 - 2x^4 + 6x^5 - 8x^6 - 50x^7 + 78x^8 + 1688x^9+...

A(A(A(x))) = x + 3x^2 + (3)x^3 - 3x^4 - x^5 + 17x^6 - 81x^7 -370x^8+...

A(A(A(A(x)))) = x + 4x^2 + 8x^3 + (4)x^4 - 12x^5 + 4x^6 + 12x^7 +...

A(A(A(A(A(x))))) = x + 5x^2 + 15x^3 + 25x^4 + (5)x^5 - 55x^6 -33x^7+...

A(A(A(A(A(A(x)))))) = x + 6x^2 + 24x^3 + 66x^4 + 106x^5 + (4)x^6 +...

Coefficients [x^n] of n-th self-composition of A(x) forms A119816:

[1,2,3,4,5,4,7,8,3,9,11,4,13,11,14,8,17,4,19,4,1,4,23,24,5,17,27,...].

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-polcoeff(G, n, x)) )))}

CROSSREFS

Cf. A119816, A119817, A112317.

Sequence in context: A180481 A110044 A032663 * A046624 A225587 A143584

Adjacent sequences:  A119812 A119813 A119814 * A119816 A119817 A119818

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 31 2006

STATUS

approved

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Last modified November 15 18:53 EST 2018. Contains 317240 sequences. (Running on oeis4.)