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A384825 G.f. A(x) satisfies -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).

%I A384825 #10 Jun 11 2025 03:12:35
%S A384825 1,1,6,54,542,5955,69114,835140,10391843,132262619,1713785727,
%T A384825 22531557603,299817809184,4030217936308,54646151953660,
%U A384825 746513545616000,10264746883787021,141955200254335604,1973170863256461516,27551902179444882489,386288077655575999571,5435910477286670671340
%N A384825 G.f. A(x) satisfies -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).
%H A384825 Paul D. Hanna, <a href="/A384825/b384825.txt">Table of n, a(n) for n = 0..300</a>
%F A384825 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A384825 (1) -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).
%F A384825 (2) -x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-5)*(n-6)) / (1 - x^n)^(n-10).
%F A384825 a(n) ~ c * d^n / n^(3/2), where d = 15.130878695250901787504105640277512076291321821... and c = 0.088532592960846902874974330489987793829057... - _Vaclav Kotesovec_, Jun 11 2025
%e A384825 G.f.: A(x) = 1 + x + 6*x^2 + 54*x^3 + 542*x^4 + 5955*x^5 + 69114*x^6 + 835140*x^7 + 10391843*x^8 + 132262619*x^9 + 1713785727*x^10 + ...
%o A384825 (PARI) {a(n) = my(A=[1,1,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
%o A384825 A[#A-5] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+10) ), #A-36)); A[n+1]}
%o A384825 for(n=0, 30, print1(a(n), ", "))
%Y A384825 Cf. A366731, A384821, A384822, A384823, A384824, A384826, A384827, A384828.
%K A384825 nonn
%O A384825 0,3
%A A384825 _Paul D. Hanna_, Jun 10 2025