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A112111
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G.f. A(x) satisfies A(A(A(A(A(x))))) = B(x) (5th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4,5}, with B(0) = 0.
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3
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1, 1, -3, 17, -115, 841, -6288, 46174, -320366, 1997348, -10216611, 32418767, 68603755, -1909624513, 15239954041, -103620859984, 1499179409198, -25808959095992, 258001631302410, -239530586418995, -25424691109062239, 84868851253494310
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OFFSET
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1,3
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LINKS
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EXAMPLE
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A(x) = x + x^2 - 3*x^3 + 17*x^4 - 115*x^5 + 841*x^6 -6288*x^7 +...
where A(A(A(A(A(x))))) =
x + 5*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 5*x^6 + 4*x^7 + 3*x^8 +...
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PROG
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(PARI) {a(n, m=5)=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)))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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