cp's OEIS Frontend

A380067 G.f. A(x) satisfies 0 = Sum_{n=-oo..+oo} (-x)^n * (A(x) - (-x)^n)^(3*n+1).

%I A380067 #6 Jan 23 2025 12:29:22
%S A380067 1,2,9,76,605,5351,49789,480401,4766086,48292018,497690157,5200558352,
%T A380067 54971657745,586748531155,6315126497084,68461134239364,
%U A380067 746869322310992,8193320926852194,90327637946283912,1000230167386765676,11120012336000921992,124071390413266176706,1388854343860145268801
%N A380067 G.f. A(x) satisfies 0 = Sum_{n=-oo..+oo} (-x)^n * (A(x) - (-x)^n)^(3*n+1).
%H A380067 Paul D. Hanna, <a href="/A380067/b380067.txt">Table of n, a(n) for n = 0..300</a>
%F A380067 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A380067 (1) 0 = Sum_{n=-oo..+oo} (-x)^n * (A(x) - (-x)^n)^(3*n+1).
%F A380067 (2) 0 = Sum_{n=-oo..+oo} x^(n*(3*n-2)) / (1 - (-x)^n*A(x))^(3*n-1).
%e A380067 G.f.: A(x) = 1 + 2*x + 9*x^2 + 76*x^3 + 605*x^4 + 5351*x^5 + 49789*x^6 + 480401*x^7 + 4766086*x^8 + 48292018*x^9 + 497690157*x^10 + ...
%e A380067 SPECIFIC VALUES.
%e A380067 A(t) = 3/2 at t = 0.083194510328352326489147821869211901063348034386178...
%e A380067 A(t) = 4/3 at t = 0.077330132914732168322332648422644564090957191059466...
%e A380067 A(t) = 5/4 at t = 0.069536731258681190910149841234109935263075324366012...
%e A380067 A(t) = 6/5 at t = 0.062338368698372988520462446903734726028227564937896...
%e A380067 A(1/12) = 1.5173629784598497189372653851252639767246421375516...
%e A380067 A(1/13) = 1.3275206734003372155231166649536738395898242302762...
%e A380067 A(1/14) = 1.2663025820443309311247755018250914700758939519601...
%e A380067 A(1/15) = 1.2281465547940615875867824117423734976415492745171...
%e A380067 A(1/16) = 1.2009676782585721612406130744065631283860104847323...
%o A380067 (PARI) {a(n) = my(V=[1]); for(i=1,n, V = concat(V,0); A = Ser(V);
%o A380067 V[#V] = -polcoef( sum(n=-#V,#V, (-x)^n * (A - (-x)^n)^(3*n+1) ),#V-1) ); H=A; V[n+1]}
%o A380067 for(n=0,30,print1(a(n),", "))
%Y A380067 Cf. A380068.
%K A380067 nonn
%O A380067 0,2
%A A380067 _Paul D. Hanna_, Jan 23 2025