A112127 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (13th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,13}, with B(0) = 0.

1, 1, -11, 193, -4043, 92233, -2188907, 52544305, -1250612651, 29060631481, -651497950667, 13997025548641, -289196932607819, 5873067677083177, -122109541297984368, 2669034419647762122, -58550172867811577842, 1127335101086707607932

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

A(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...
where A(A(A(A(A(A(A(A(A(A(A(A(A(x))))))))))))) =
x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 + 13*x^7 +...
is the g.f. of A112126.

Prog

(PARI) {a(n, m=13)=local(F=x+x^2+x*O(x^n), G); if(n<1, 0, for(k=3, n, G=F+x*O(x^k); for(i=1, m-1, G=subst(F, x, G)); F=F-((polcoeff(G, k)-1)\m)*x^k); return(polcoeff(F, n, x)))}

Crossrefs

Cf. A112126, A112104-A112125.

Sequence in context: A072290 A258295 A213691 * A364942 A142996 A201185

Adjacent sequences: A112124 A112125 A112126 * A112128 A112129 A112130

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved