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A373220 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 6^j)).

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%I A373220 #12 May 31 2024 14:35:38
%S A373220 1,1,1,2,2,3,5,6,7,10,12,15,20,24,29,37,44,53,67,79,94,115,135,160,
%T A373220 193,226,265,315,367,428,505,585,678,792,913,1054,1225,1406,1614,1862,
%U A373220 2129,2436,2797,3187,3630,4147,4709,5347,6084,6887,7793,8832,9968,11247,12706,14301,16089,18116,20337
%N A373220 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 6^j)).
%F A373220 G.f.: Product_{k>=1} (1 + x^k)^A373216(k).
%F A373220 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^6).
%o A373220 (PARI) my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(valuation(k, 6)+1)))
%Y A373220 Cf. A000041, A174065, A327726, A373219, A373221.
%Y A373220 Cf. A000009, A373216.
%K A373220 nonn
%O A373220 0,4
%A A373220 _Seiichi Manyama_, May 28 2024