cp's OEIS Frontend

A102346 Number of partitions of 2n in which odd parts and multiples of 3 and 5 occur with even multiplicities. There is no restriction on the other even parts.

%I A102346 #18 Sep 01 2015 06:30:26
%S A102346 1,2,4,7,12,19,30,46,69,101,146,208,293,408,563,769,1042,1401,1871,
%T A102346 2482,3273,4291,5596,7261,9378,12057,15437,19684,25005,31648,39919,
%U A102346 50184,62890,78573,97883,121597,150653,186169,229487,282204,346230,423831,517706
%N A102346 Number of partitions of 2n in which odd parts and multiples of 3 and 5 occur with even multiplicities. There is no restriction on the other even parts.
%H A102346 Alois P. Heinz, <a href="/A102346/b102346.txt">Table of n, a(n) for n = 0..10000</a>
%H A102346 Noureddine Chair, <a href="http://arxiv.org/abs/hep-th/0409011">Partition Identities From Partial Supersymmetry</a>, arXiv:hep-th/0409011v1, 2004.
%F A102346 G.f.: Product((1+x^k)*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))), k>=1).
%F A102346 a(n) ~ exp(Pi*sqrt(38*n/5)/3) * sqrt(19) / (12*sqrt(5)*n). - _Vaclav Kotesovec_, Sep 01 2015
%F A102346 G.f.: (E(2)*E(3)*E(5)*E(30)) / (E(1)^2*E(6)*E(10)*E(15)) where E(k) = prod(n>=1, 1-q^k ). - _Joerg Arndt_, Sep 01 2015
%e A102346 a(5) = 19: [8,2], [8,1,1], [5,5], [4,4,2], [4,4,1,1], [4,2,2,2], [4,2,2,1,1], [4,2,1,1,1,1], [4,3,3], [3,3,2,2], [3,3,2,1,1], [3,3,1,1,1,1], [4,1,1,1,1,1,1], [2,2,2,2,2], [2,2,2,2,1,1], [2,2,2,1,1,1,1], [2,2,1,1,1,1,1,1], [2,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1].
%t A102346 nmax = 50; CoefficientList[Series[Product[(1+x^k)*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 01 2015 *)
%o A102346 (PARI) q='q+O('q^33); E(k)=eta(q^k);
%o A102346 Vec( (E(2)*E(3)*E(5)*E(30)) / (E(1)^2*E(6)*E(10)*E(15)) ) \\ _Joerg Arndt_, Sep 01 2015
%Y A102346 Cf. A098151.
%K A102346 nonn
%O A102346 0,2
%A A102346 _Noureddine Chair_, Feb 21 2005
%E A102346 Corrected by Vladeta Jovovic, Feb 21 2005
%E A102346 Offset and example corrected by _Vaclav Kotesovec_, Sep 01 2015