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A295535 G.f. A(x) satisfies: A(x) = 1 + x*A(x)^5 - x^2/A(x)^19. 1

%I #7 Jan 13 2018 04:41:23

%S 1,1,4,49,221,3111,17110,286578,1784529,29714413,193118947,3253370410,

%T 22144312913,376516950886,2659177494183,45125258300214,

%U 328077052846719,5547886336336596,41395900427450752,696487627072615303,5318129715505774090,88895036913883332534,693010823211937855758,11500480362344463647316,91380901216880290639953,1504829325697181753357643,12169760738275049654025420

%N G.f. A(x) satisfies: A(x) = 1 + x*A(x)^5 - x^2/A(x)^19.

%C Note that G(x) such that G(x) = 1 + x*G(x)^5 - x^2/G(x)^20 has negative coefficients.

%H Paul D. Hanna, <a href="/A295535/b295535.txt">Table of n, a(n) for n = 0..500</a>

%F G.f. A(x) satisfies: x^2 = A(x)^19 - A(x)^20 + x*A(x)^24.

%e G.f. A(x) = 1 + x + 4*x^2 + 49*x^3 + 221*x^4 + 3111*x^5 + 17110*x^6 + 286578*x^7 + 1784529*x^8 + 29714413*x^9 + 193118947*x^10 + 3253370410*x^11 + 22144312913*x^12 + 376516950886*x^13 + 2659177494183*x^14 + 45125258300214*x^15 +...

%e such that A(x) = 1 + x*A(x)^5 - x^2/A(x)^19.

%e RELATED SERIES.

%e A(x)^5 = 1 + 5*x + 30*x^2 + 335*x^3 + 2370*x^4 + 25926*x^5 + 209970*x^6 + 2500335*x^7 + 22105350*x^8 + 268963090*x^9 + 2469780029*x^10 +...

%e 1/A(x)^19 = 1 - 19*x + 114*x^2 - 741*x^3 + 8816*x^4 - 76608*x^5 + 715806*x^6 - 7609063*x^7 + 75844143*x^8 - 783590381*x^9 + 8287390987*x^10 +...

%e A(x)^19 = 1 + 19*x + 247*x^2 + 3268*x^3 + 39197*x^4 + 464322*x^5 + 5337442*x^6 + 61643904*x^7 + 703546554*x^8 + 8087101233*x^9 + 92320933272*x^10 +...

%e A(x)^20 = 1 + 20*x + 270*x^2 + 3640*x^3 + 44605*x^4 + 536004*x^5 + 6249490*x^6 + 72861600*x^7 + 839576970*x^8 + 9713635800*x^9 + 111672521472*x^10 +...

%e A(x)^24 = 1 + 24*x + 372*x^2 + 5408*x^3 + 71682*x^4 + 912048*x^5 + 11217696*x^6 + 136030416*x^7 + 1626534567*x^8 + 19351588200*x^9 + 228642682668*x^10 +...

%e where x^2 = A(x)^19 - A(x)^20 + x*A(x)^24.

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^5 - x^2/A^19 +x*O(x^n)); polcoeff(G=A, n)}

%o for(n=0, 40, print1(a(n), ", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 23 2017

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