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A372956 G.f. A(x) satisfies A(x)^5 = A(x^5) / (1 - 5*x)^5 with A(0)=1.

%I A372956 #23 Jul 05 2024 02:09:37
%S A372956 1,5,25,125,625,3126,15630,78150,390750,1953750,9768753,48843765,
%T A372956 244218825,1221094125,6105470625,30527353136,152636765680,
%U A372956 763183828400,3815919142000,19079595710000,95397978550044,476989892750220,2384949463751100,11924747318755500,59623736593777500
%N A372956 G.f. A(x) satisfies A(x)^5 = A(x^5) / (1 - 5*x)^5 with A(0)=1.
%C A372956 Euler transform of 5 * A054662(n).
%H A372956 Seiichi Manyama, <a href="/A372956/b372956.txt">Table of n, a(n) for n = 0..1000</a>
%H A372956 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%F A372956 G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A054662(k) )^5.
%e A372956 A(x)^5 = 1 + 25*x + 375*x^2 + 4375*x^3 + 43750*x^4 + 393755*x^5 + ... .
%o A372956 (PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
%o A372956 my(N=30, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 5))^5)
%Y A372956 Cf. A372870, A372957.
%Y A372956 Cf. A054662, A372535.
%K A372956 nonn
%O A372956 0,2
%A A372956 _Seiichi Manyama_, Jul 04 2024