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A373219 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 5^j)).

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%I A373219 #13 May 31 2024 14:35:30
%S A373219 1,1,1,2,2,4,5,6,8,10,14,17,21,26,32,42,50,60,74,88,109,130,154,184,
%T A373219 218,263,309,363,428,500,593,690,802,936,1084,1266,1463,1687,1948,
%U A373219 2242,2590,2970,3403,3900,4456,5107,5820,6626,7546,8572,9755,11059,12523,14180,16028,18133,20455,23056,25978
%N A373219 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 5^j)).
%F A373219 G.f.: Product_{k>=1} (1 + x^k)^A055457(k).
%F A373219 Let A(x) be the g.f. of this sequence, and B(x) be the g.f. of A000009, then B(x) = A(x)/A(x^5).
%o A373219 (PARI) my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(valuation(k, 5)+1)))
%Y A373219 Cf. A000041, A174065, A327726, A373220, A373221.
%Y A373219 Cf. A000009, A055457.
%K A373219 nonn
%O A373219 0,4
%A A373219 _Seiichi Manyama_, May 28 2024