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A384826 G.f. A(x) satisfies 1/x^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).

%I A384826 #10 Jun 11 2025 03:14:48
%S A384826 1,1,7,73,861,11112,151828,2159179,31627690,473917665,7230164079,
%T A384826 111926802631,1753762735460,27760507986844,443257137593369,
%U A384826 7130838718144623,115469073853104486,1880570694656739472,30784302913287253256,506228988080918570208,8358750672258509735440,138528877561300962357350
%N A384826 G.f. A(x) satisfies 1/x^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).
%H A384826 Paul D. Hanna, <a href="/A384826/b384826.txt">Table of n, a(n) for n = 0..300</a>
%F A384826 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A384826 (1) 1/x^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).
%F A384826 (2) x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-6)*(n-7)) / (1 - x^n)^(n-12).
%F A384826 a(n) ~ c * d^n / n^(3/2), where d = 17.821078213117779013059276484226766696509894506... and c = 0.072486824411461280676499747682168909434267... - _Vaclav Kotesovec_, Jun 11 2025
%e A384826 G.f.: A(x) = 1 + x + 7*x^2 + 73*x^3 + 861*x^4 + 11112*x^5 + 151828*x^6 + 2159179*x^7 + 31627690*x^8 + 473917665*x^9 + 7230164079*x^10 + ...
%o A384826 (PARI) {a(n) = my(A=[1,1,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
%o A384826 A[#A-6] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+12) ), #A-49)); A[n+1]}
%o A384826 for(n=0, 30, print1(a(n), ", "))
%Y A384826 Cf. A366731, A384821, A384822, A384823, A384824, A384825, A384827, A384828.
%K A384826 nonn
%O A384826 0,3
%A A384826 _Paul D. Hanna_, Jun 10 2025