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A384823 G.f. A(x) satisfies -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).

%I A384823 #10 Jun 11 2025 03:07:29
%S A384823 1,1,4,28,173,1262,9593,75928,618342,5149640,43650123,375347585,
%T A384823 3266282211,28709930633,254526671024,2273271614848,20435110855838,
%U A384823 184745786960642,1678668998195885,15321962225034079,140418372363945954,1291587696225346583,11919771215919819476,110338977972166474055
%N A384823 G.f. A(x) satisfies -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).
%H A384823 Paul D. Hanna, <a href="/A384823/b384823.txt">Table of n, a(n) for n = 0..300</a>
%F A384823 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A384823 (1) -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).
%F A384823 (2) -x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-3)*(n-4)) / (1 - x^n)^(n-6).
%F A384823 a(n) ~ c * d^n / n^(3/2), where d = 9.887717015668710733345454711929087306... and c = 0.160435430066288197856237263106693... - _Vaclav Kotesovec_, Jun 11 2025
%e A384823 G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 173*x^4 + 1262*x^5 + 9593*x^6 + 75928*x^7 + 618342*x^8 + 5149640*x^9 + 43650123*x^10 + ...
%o A384823 (PARI) {a(n) = my(A=[1,1,0,0,0]); for(i=1, n, A = concat(A, 0);
%o A384823 A[#A-3] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+6) ), #A-16)); A[n+1]}
%o A384823 for(n=0, 30, print1(a(n), ", "))
%Y A384823 Cf. A366731, A384821, A384822, A384824, A384825, A384826, A384827, A384828.
%K A384823 nonn
%O A384823 0,3
%A A384823 _Paul D. Hanna_, Jun 10 2025