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%I A363315 #12 Jun 09 2023 21:27:13
%S A363315 6,50,950,21350,530700,14067650,389701050,11147799700,326779719500,
%T A363315 9764739197800,296342706620800,9108989853295550,283002934668287000,
%U A363315 8872796279035164100,280368062326854982450,8919740526808334086550,285476263708658548421000,9185078302539674382641450
%N A363315 Expansion of g.f. A(x) satisfying 1/5 = Sum_{n=-oo..+oo} x^n * (A(x) - x^n)^(n-1), with a(0) = 6.
%C A363315 a(n) == 0 (mod 5^2) for n > 0.
%H A363315 Paul D. Hanna, <a href="/A363315/b363315.txt">Table of n, a(n) for n = 0..200</a>
%F A363315 G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
%F A363315 (1) 1/5 = Sum_{n=-oo..+oo} x^n * (A(x) - x^n)^(n-1).
%F A363315 (2) 1/5 = Sum_{n=-oo..+oo} (-1)^(n+1) * x^(n^2) / (1 - x^n*A(x))^(n+1).
%F A363315 (3) A(x)/5 = Sum_{n=-oo..+oo} x^(2*n) * (A(x) - x^n)^(n-1).
%F A363315 (4) A(x)/5 = Sum_{n=-oo..+oo} (-1)^(n+1) * x^(n*(n-1)) / (1 - x^n*A(x))^(n+1).
%e A363315 G.f.: A(x) = 6 + 50*x + 950*x^2 + 21350*x^3 + 530700*x^4 + 14067650*x^5 + 389701050*x^6 + 11147799700*x^7 + 326779719500*x^8 + ...
%o A363315 (PARI) {a(n) = my(A=[6]); for(i=1,n, A = concat(A,0);
%o A363315 A[#A] = polcoeff(-5  + 5^2*sum(m=-#A, #A, x^m * (Ser(A) - x^m)^(m-1) ), #A-1););A[n+1]}
%o A363315 for(n=0,30,print1(a(n),", "))
%Y A363315 Cf. A357227, A363141, A363312, A363313, A363314.
%K A363315 nonn
%O A363315 0,1
%A A363315 _Paul D. Hanna_, May 28 2023

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