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A173241 Euler transform of A051064, the ruler function sequence for k=3.

%I A173241 #12 Apr 29 2021 08:37:59
%S A173241 1,1,2,4,6,9,16,22,33,51,71,100,147,199,275,384,515,692,944,1242,1645,
%T A173241 2186,2847,3706,4848,6231,8019,10330,13153,16729,21305,26864,33858,
%U A173241 42658,53366,66668,83277,103378,128200,158846,195895,241237,296860,363796,445285,544465,663520
%N A173241 Euler transform of A051064, the ruler function sequence for k=3.
%C A173241 Let P(x) = polcoeff A000041: (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...) and
%C A173241 A(x) = polcoeff A173241: (1 + x + 2x^2 + 4x^3 + 6x^4 + 9x^5 + ...); then
%C A173241 P(x) = A(x) / A(x^3).
%C A173241 A092119 = Euler transform of the ruler function for k=2: A001511.
%H A173241 Seiichi Manyama, <a href="/A173241/b173241.txt">Table of n, a(n) for n = 0..10000</a>
%F A173241 G.f.: 1/Product_{k>=0} P(x^(3^k)) where P(x)=Product_{k>=1} (1-x^k). - _Joerg Arndt_, Jun 21 2011
%F A173241 Euler transform of A051064, where A051064 = the ruler function for k=3:
%F A173241 (1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, ...).
%e A173241 Equals 1/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^5)*(1-x^6)^2*(1-x^7)*...); where in (1-x)^k, k = A051064: (1, 1, 2, 1, 1, 2, 1, 1, 3, ...).
%o A173241 (PARI)  N=66; x='x+O('x^N); /* that many terms */
%o A173241 gf=1/prod(e=0, ceil(log(N)/log(3)), eta(x^(3^e)));
%o A173241 Vec(gf) /* show terms */ /* _Joerg Arndt_, Jun 21 2011 */
%Y A173241 Cf. A000041, A001511, A051064, A092119, A173238, A173239.
%K A173241 nonn
%O A173241 0,3
%A A173241 _Gary W. Adamson_, Feb 13 2010
%E A173241 More terms from _Joerg Arndt_, Jun 21 2011