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A372870 G.f. A(x) satisfies A(x)^3 = A(x^3) / (1 - 3*x)^3 with A(0)=1.

%I A372870 #22 Jul 05 2024 02:10:17
%S A372870 1,3,9,28,84,252,758,2274,6822,20471,61413,184239,552729,1658187,
%T A372870 4974561,14923714,44771142,134313426,402940361,1208821083,3626463249,
%U A372870 10879389971,32638169913,97914509739,293743529832,881230589496,2643691768488,7931075307172
%N A372870 G.f. A(x) satisfies A(x)^3 = A(x^3) / (1 - 3*x)^3 with A(0)=1.
%C A372870 Euler transform of 3 * A046211(n).
%H A372870 Seiichi Manyama, <a href="/A372870/b372870.txt">Table of n, a(n) for n = 0..1000</a>
%H A372870 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%F A372870 G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A046211(k) )^3.
%e A372870 A(x)^3 = 1 + 9*x + 54*x^2 + 273*x^3 + 1242*x^4 + 5265*x^5 + 21231*x^6 + ... .
%o A372870 (PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
%o A372870 my(N=30, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 3))^3)
%Y A372870 Cf. A372956, A372957.
%Y A372870 Cf. A046211, A271929.
%K A372870 nonn
%O A372870 0,2
%A A372870 _Seiichi Manyama_, Jul 04 2024