Search: id:A107742
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%I A107742
%S A107742 1,1,2,4,6,10,17,25,38,59,86,125,184,260,369,524,726,1005,1391,1894,
%T A107742 2576,3493,4687,6272,8373,11090,14647,19294,25265,32991,42974,55705,
%U A107742 72025,92895,119349,152965,195592,249280,316991,402215,508932,642598
%N A107742 G.f.: Product(Product(1+x^(i*j),i=1..infinity),j=1..infinity).
%H A107742 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A107742 Euler transform of A001227. Weigh transform of A000005.
%F A107742 G.f. satisfies: log(A(x)) = Sum_{n>=1} A109386(n)/n*x^n, where A109386(n) 
               = Sum_{d|n} d*Sum_{m|d} (m mod 2). - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jun 26 2005
%F A107742 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*x^n/(1-x^(2n)) /n ). [From Paul 
               D. Hanna (pauldhanna(AT)juno.com), Mar 28 2009]
%o A107742 (PARI) a(n)=polcoeff(prod(k=1,n,prod(j=1,n\k,1+x^(j*k)+x*O(x^n))),n) 
               (Hanna)
%o A107742 (PARI) 1/prod(j=0,N, eta(x^(2*j+1))); Vec(%) - Joerg Arndt (arndt(AT)jjj.de), 
               May 03 2008
%o A107742 (PARI) prod(j=1,N,(1+x^j)^numdiv(j)); Vec(%) - Joerg Arndt (arndt(AT)jjj.de), 
               May 03 2008
%o A107742 (PARI) {a(n)=if(n==0,1,polcoeff(exp(sum(m=1,n,sigma(m)*x^m/(1-x^(2*m)+x*O(x^n))/
               m)),n))} [From Paul D. Hanna (pauldhanna(AT)juno.com), Mar 28 2009]
%Y A107742 Cf. A006171, A109386.
%Y A107742 Sequence in context: A048833 A070689 A091611 this_sequence A158510 A004695 
               A014216
%Y A107742 Adjacent sequences: A107739 A107740 A107741 this_sequence A107743 A107744 
               A107745
%K A107742 easy,nonn
%O A107742 0,3
%A A107742 Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 11 2005
%E A107742 More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jun 26 2005

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