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%I #12 Jul 28 2022 08:19:57
%S 1,2,5,12,37,121,419,1510,5604,21261,82110,321662,1275077,5104886,
%T 20611814,83834609,343164051,1412600336,5843868040,24283650452,
%U 101312783192,424212909937,1782086178267,7508852850710,31725558330499,134381573170076,570532128884181
%N G.f. A(x) satisfies: 0 = Sum_{n=-oo..+oo} x^(n*(n-1)/2) * (x^n - A(x))^n.
%H Paul D. Hanna, <a href="/A355861/b355861.txt">Table of n, a(n) for n = 0..400</a>
%F G.f. A(x) satisfies:
%F (1) 0 = Sum_{n=-oo..+oo} x^(n*(n-1)/2) * (x^n - A(x))^n.
%F (2) 0 = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) / (1 - A(x)*x^n)^n.
%F a(n) ~ c * d^n / n^(3/2), where d = 4.4984524719254844098592086179118472526... and c = 0.813659600743159302516036718242855... - _Vaclav Kotesovec_, Jul 23 2022
%F A(1/d) = 2.6481605623378565... where 1/d = 0.2222986696516029605295343... and d is the value given above by _Vaclav Kotesovec_. - _Paul D. Hanna_, Jul 28 2022
%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 37*x^4 + 121*x^5 + 419*x^6 + 1510*x^7 + 5604*x^8 + 21261*x^9 + 82110*x^10 + 321662*x^11 + ...
%e where
%e 0 = ... + x^6/(1/x^3 - A(x))^3 + x^3/(1/x^2 - A(x))^2 + x/(1/x - A(x)) + 1 + (x - A(x)) + x*(x^2 - A(x))^2 + x^3*(x^3 - A(x))^3 + x^6*(x^4 - A(x))^4 + ... + x^(n*(n-1)/2)*(x^n - A(x))^n + ...
%e Specific values.
%e A(0.20604788...) = 2.
%e A(1/5) = 1.9097493689592466...
%o (PARI) {a(n) = my(A=[1],M); for(i=1,n, A=concat(A,0); M = ceil(sqrt(2*(#A)+9));
%o A[#A] = polcoeff( sum(m=-M,M, x^(m*(m-1)/2) * (x^m - Ser(A))^m ), #A-1));A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 22 2022
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