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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.
3
1, 2, 4, 7, 12, 19, 30, 46, 69, 101, 146, 208, 293, 408, 563, 769, 1042, 1401, 1871, 2482, 3273, 4291, 5596, 7261, 9378, 12057, 15437, 19684, 25005, 31648, 39919, 50184, 62890, 78573, 97883, 121597, 150653, 186169, 229487, 282204, 346230, 423831, 517706
OFFSET
0,2
LINKS
Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.
FORMULA
G.f.: Product((1+x^k)*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))), k>=1).
a(n) ~ exp(Pi*sqrt(38*n/5)/3) * sqrt(19) / (12*sqrt(5)*n). - Vaclav Kotesovec, Sep 01 2015
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
EXAMPLE
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].
MATHEMATICA
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 *)
PROG
(PARI) q='q+O('q^33); E(k)=eta(q^k);
Vec( (E(2)*E(3)*E(5)*E(30)) / (E(1)^2*E(6)*E(10)*E(15)) ) \\ Joerg Arndt, Sep 01 2015
CROSSREFS
Cf. A098151.
Sequence in context: A008609 A264392 A100823 * A333148 A343661 A342229
KEYWORD
nonn
AUTHOR
Noureddine Chair, Feb 21 2005
EXTENSIONS
Corrected by Vladeta Jovovic, Feb 21 2005
Offset and example corrected by Vaclav Kotesovec, Sep 01 2015
STATUS
approved