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A277300
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G.f. satisfies: A(x - A(x)^2) = x + 4*A(x)^2.
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13
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1, 5, 60, 1000, 19970, 448160, 10926360, 283651245, 7740058300, 220046970860, 6476695275680, 196438030797880, 6117627849485360, 195082685133612800, 6355848358118392400, 211189970909192038500, 7146354688384980282000, 245970478274041025623200, 8602606263466490521359400, 305460999044315834902424200, 11003870605124169641012461600
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f. A(x) also satisfies:
(1) A(x) = x + 5 * A( 4*x/5 + A(x)/5 )^2.
(2) A(x) = -4*x + 5 * Series_Reversion(x - A(x)^2).
(3) R(x) = -x/4 + 5/4 * Series_Reversion(x + 4*A(x)^2), where R(A(x)) = x.
(4) R( sqrt( x/5 - R(x)/5 ) ) = x/5 + 4*R(x)/5, where R(A(x)) = x.
a(n) = Sum_{k=0..n-1} A277295(n,k) * 5^(n-k-1).
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EXAMPLE
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G.f.: A(x) = x + 5*x^2 + 60*x^3 + 1000*x^4 + 19970*x^5 + 448160*x^6 + 10926360*x^7 + 283651245*x^8 + 7740058300*x^9 + 220046970860*x^10 +...
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MATHEMATICA
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m = 22; A[_] = 0;
Do[A[x_] = x + 5 A[4x/5 + A[x]/5]^2 + O[x]^m // Normal, {m}];
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PROG
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(PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x - F^2) - 4*F^2, #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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