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 A112573 G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9. 0

%I

%S 1,1,0,0,2,-2,5,-6,5,3,-26,70,-141,221,-229,-18,891,-2914,6524,-11238,

%T 13690,-4214,-37619,145018,-353534,657080,-895234,534007,1654246,

%U -7840402,20737566,-41200153,61402057,-50500722,-68352913,441195837,-1272153666,2690651374

%N G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9.

%C A110640 is formed from every third term of A083949, which also consists entirely of numbers 1 through 9.

%F G.f. A(x) satisfies: A(x)^9 (mod 27) = g.f. of A083949.

%e A(x) = 1 + x + 2*x^4 - 2*x^5 + 5*x^6 - 6*x^7 + 5*x^8 + 3*x^9 +...

%e A(x)^3 = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 + 6*x^7 +...

%e A(x)^9 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 + 489*x^6 +..

%e A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6+..

%e G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 + 9*x^7 +...

%e where G(x) is the g.f. of A083949.

%o (PARI) {a(n)=local(d=3,m=9,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break))); polcoeff(Ser(vector(n+1,i,polcoeff(A,d*(i-1))))^(1/3),n)}

%Y Cf. A110640, A083949.

%K sign

%O 0,5

%A _Paul D. Hanna_, Sep 14 2005

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Last modified December 8 02:32 EST 2021. Contains 349590 sequences. (Running on oeis4.)