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.
%I A372957 #26 Jul 05 2024 02:10:33
%S A372957 1,2,5,10,22,44,91,182,370,740,1490,2980,5979,11958,23950,47900,95865,
%T A372957 191730,383580,767160,1534549,3069098,6138628,12277256,24555341,
%U A372957 49110682,98222947,196445894,392894839,785789678,1571585230,3143170460,6286352290,12572704580,25145431172
%N A372957 G.f. A(x) satisfies A(x)^2 = A(x^2) / (1 - 2*x)^2 with A(0)=1.
%C A372957 Euler transform of 2 * A000048(n).
%H A372957 Seiichi Manyama, <a href="/A372957/b372957.txt">Table of n, a(n) for n = 0..1000</a>
%H A372957 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%F A372957 G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A000048(k) )^2.
%e A372957 A(x)^2 = 1 + 4*x + 14*x^2 + 40*x^3 + 109*x^4 + 276*x^5 + 678*x^6 + ... .
%o A372957 (PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
%o A372957 my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 2))^2)
%Y A372957 Cf. A372870, A372956.
%Y A372957 Cf. A000048, A123916.
%K A372957 nonn
%O A372957 0,2
%A A372957 _Seiichi Manyama_, Jul 04 2024