Search: id:A101277
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%I A101277
%S A101277 1,2,3,6,10,16,25,38,57,84,121,172,243,338,465,636,862,1158,1546,2050,
%T A101277 2702,3542,4616,5986,7729,9932,12707,16196,20563,26010,32788,41194,
%U A101277 51591,64418,80195,99558,123269,152226,187514,230434,282519,345596
%N A101277 Number of partitions of 2n in which all odd parts occur with multiplicity 
               2. There is no restriction on the even parts.
%C A101277 This is also A080054 times 1/product_{k>0}(1-x^(2k))
%C A101277 There are no partitions of 2n+1 in which all odd parts occur with multiplicity 
               2. - Michael Somos Oct 27 2008
%D A101277 Noureddine Chair, Partition Identities From Partial Supersymmetry, hep-th/
               0409011
%F A101277 Euler transform of period 4 sequence [2, 0, 2, 1, ...]. - Michael Somos 
               Feb 10 2005
%F A101277 G.f.:=1/theta_4(0, x)product_{k>0}(1+x^(2k))= theta_4(0, x^2)/theta_4(0, 
               x)product_{k>0}(1-x^(2k))= 1/product_{k>0}(1-x^(2k-1))^2(1-x^(4k)).
%F A101277 Expansion of 1 / (psi(-q) * chi(-q)) in powers of q where psi(), chi() 
               are Ramanujan theta functions. - Michael Somos Oct 27 2008
%F A101277 Expansion of q^(1/12) * eta(q^2)^2 / (eta(q)^2 * eta(q^4)) in powers 
               of q. - Michael Somos Oct 27 2008
%e A101277 E.g. 12 = 10 + 2 = 10 + 1 + 1 = 8 + 4 = 8 + 2 + 2 = 8 + 2 + 1 + 1 = 6 
               + 6 = 6 + 4 + 2 = 6 + 4 + 1 + 1 = 6 + 3 + 3 = 6 + 2 + 2 + 2 = 6 + 
               2 + 2 + 1 + 1 = 5 + 5 + 2 = 5 + 5 + 1 + 1 = 4 + 4 + 4 = 4 + 4 + 2 
               + 2 = 4 + 4 + 2 + 1 + 1 = 4 + 3 + 3 + 2 = 4 + 3 + 3 + 1 + 1 = 4 + 
               2 + 2 + 2 + 2 = 4 + 2 + 2 + 2 + 1 + 1 = 3 + 3 + 2 + 2 + 2 = 3 + 3 
               + 2 + 2 + 1 + 1 = 2 + 2 + 2 + 2 + 2 + 2 = 2 + 2 + 2 + 2 + 2 + 1 + 
               1.
%e A101277 1/q + 2*q^11 + 3*q^23 + 6*q^35 + 10*q^47 + 16*q^59 + 25*q^71 + 38*q^83 
               + ...
%p A101277 series(product(1/((1-x^(2*k-1))^2*(1-x^(4*k))),k=1..100),x=0,100);
%o A101277 (PARI) {a(n)=local(A); if(n<0,0,A=x*O(x^n); polcoeff( eta(x^2+A)^2/eta(x+A)^2/
               eta(x^4+A), n))} /* Michael Somos Feb 10 2005 */
%Y A101277 Cf. A015128, A098151, A080054.
%Y A101277 Sequence in context: A075623 A024801 A146163 this_sequence A023655 A023561 
               A034419
%Y A101277 Adjacent sequences: A101274 A101275 A101276 this_sequence A101278 A101279 
               A101280
%K A101277 nonn
%O A101277 0,2
%A A101277 Noureddine Chair (n.chair(AT)rocketmail.com), Dec 20 2004; revised Jan 
               05 2005

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