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%I #20 May 31 2024 14:36:00
%S 1,1,2,3,6,8,13,18,29,39,57,77,112,148,205,271,373,485,649,841,1116,
%T 1431,1865,2379,3080,3896,4979,6268,7961,9953,12524,15585,19505,24135,
%U 29984,36943,45678,56007,68841,84080,102912,125164,152449,184756,224184,270691,327094,393675
%N Expansion of 1/Product_{k>=1} (1 - x^k)^(valuation(k,4) + 1).
%F G.f.: A(x) = 1/Product_{i>=1, j>=0} (1 - x^(i * 4^j)).
%F Let A(x) be the g.f. of this sequence, and P(x) be the g.f. of A000041, then P(x) = A(x)/A(x^4).
%o (PARI) my(N=50, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^k)^(valuation(k, 4)+1)))
%Y Cf. A092119, A173241, A373296, A373297, A373298.
%Y Cf. A000041, A115362, A174065.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 31 2024