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A384828 G.f. A(x) satisfies 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).

%I A384828 #10 Jun 11 2025 03:18:38
%S A384828 1,1,9,120,1839,30862,548783,10160786,193811734,3782270289,
%T A384828 75158649892,1515578476370,30935212293083,637920390487505,
%U A384828 13269865608471203,278121828806207328,5867506406619195047,124502776024601555996,2655381364988431518262,56892952987400631546208,1223972213493916563960331
%N A384828 G.f. A(x) satisfies 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).
%H A384828 Paul D. Hanna, <a href="/A384828/b384828.txt">Table of n, a(n) for n = 0..250</a>
%F A384828 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A384828 (1) 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).
%F A384828 (2) x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-8)*(n-9)) / (1 - x^n)^(n-16).
%F A384828 a(n) ~ c * d^n / n^(3/2), where d = 23.2218466497883684132359544378917382382303363986... and c = 0.05318473987345007866210446949223464954972731... - _Vaclav Kotesovec_, Jun 11 2025
%e A384828 G.f.: A(x) = 1 + x + 9*x^2 + 120*x^3 + 1839*x^4 + 30862*x^5 + 548783*x^6 + 10160786*x^7 + 193811734*x^8 + 3782270289*x^9 + 75158649892*x^10 + ...
%o A384828 (PARI) {a(n) = my(A=[1,1,0,0,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
%o A384828 A[#A-8] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+16) ), #A-81)); A[n+1]}
%o A384828 for(n=0, 30, print1(a(n), ", "))
%Y A384828 Cf. A366731, A384821, A384822, A384823, A384824, A384825, A384826, A384827.
%K A384828 nonn
%O A384828 0,3
%A A384828 _Paul D. Hanna_, Jun 10 2025