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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A307067 Expansion of 1/(2 - Product_{k>=2} (1 + x^k)).

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%I A307067 #12 Jan 25 2024 04:56:23
%S A307067 1,0,1,1,2,4,6,12,19,36,60,108,187,328,576,1005,1765,3084,5408,9461,
%T A307067 16575,29017,50812,88977,155792,272813,477684,836466,1464654,2564685,
%U A307067 4490833,7863610,13769463,24110774,42218847,73926591,129448088,226667986,396903536,694991728
%N A307067 Expansion of 1/(2 - Product_{k>=2} (1 + x^k)).
%C A307067 Invert transform of A025147.
%H A307067 G. C. Greubel, <a href="/A307067/b307067.txt">Table of n, a(n) for n = 0..1000</a>
%F A307067 a(0) = 1; a(n) = Sum_{k=1..n} A025147(k)*a(n-k).
%F A307067 From _G. C. Greubel_, Jan 24 2024: (Start)
%F A307067 G.f.: (1+x)/(2*(1+x) - QP(x^2)/QP(x)), where QP(x) = QPochhammer(x).
%F A307067 G.f.: (1+x)/(2*(1+x) - x^(1/24)*eta(x^2)/eta(x)), where eta(x) is the Dedekind eta function. (End)
%p A307067 a:=series(1/(2-mul((1+x^k),k=2..100)),x=0,40): seq(coeff(a,x,n),n=0..39); # _Paolo P. Lava_, Apr 03 2019
%t A307067 nmax = 39; CoefficientList[Series[1/(2 - Product[(1 + x^k), {k, 2, nmax}]), {x, 0, nmax}], x]
%o A307067 (Magma)
%o A307067 m:=80;
%o A307067 R<x>:=PowerSeriesRing(Integers(), m);
%o A307067 Coefficients(R!( 1/(2 - (&*[1+x^j: j in [2..m+2]])) )); // _G. C. Greubel_, Jan 24 2024
%o A307067 (SageMath)
%o A307067 m=80;
%o A307067 def f(x): return 1/( 2 - product(1+x^j for j in range(2, m+3)) )
%o A307067 def A307067_list(prec):
%o A307067     P.<x> = PowerSeriesRing(QQ, prec)
%o A307067     return P( f(x) ).list()
%o A307067 A307067_list(m) # _G. C. Greubel_, Jan 24 2024
%Y A307067 Cf. A025147, A055887, A299106, A304969, A307057, A307060, A317536.
%K A307067 nonn
%O A307067 0,5
%A A307067 _Ilya Gutkovskiy_, Mar 22 2019