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%I #9 Jul 10 2018 08:02:57
%S 1,8,51,305,1770,10236,58947,340164,1964863,11374720,65966318,
%T 383294335,2230877428,13005068804,75923905800,443837524793,
%U 2597761611894,15221637661064,89283411393018,524194446429830,3080311943556785,18115458477472312,106618075368243534,627937320952669230,3700709501165664301,21823188287212298688,128765319930166601616,760171656002439325155,4489959180983688448616,26532501571577231904204
%N a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 4 + 1/x^m)^m for n >= 1.
%C The coefficient of 1/x^n in Sum_{m>=0} (x^m + 4 + 1/x^m)^m equals a(n) for n > 0, while the constant term in the sum increases without limit.
%C a(n) = Sum_{k=0..n-1} A316590(n,k) * 4^k for n >= 1.
%H Paul D. Hanna, <a href="/A316594/b316594.txt">Table of n, a(n) for n = 1..260</a>
%F a(n) ~ 2^(n - 1/2) * 3^(n + 1/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jul 10 2018
%e G.f.: A(x) = x + 8*x^2 + 51*x^3 + 305*x^4 + 1770*x^5 + 10236*x^6 + 58947*x^7 + 340164*x^8 + 1964863*x^9 + 11374720*x^10 + ...
%e such that Sum_{m>=0} (x^m + 4 + 1/x^m)^m = A(x) + A(1/x) + (infinity)*x^0.
%o (PARI) {a(n) = polcoeff( sum(m=1,n, (x^-m + 4 + x^m)^m +x*O(x^n)), n,x)}
%o for(n=1,40, print1(a(n),", "))
%Y Cf. A304638, A316590, A316591, A316592, A316593, A316595.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jul 08 2018
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