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A328744
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Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^q(k), where q(k) = number of partitions of k into distinct parts (A000009).
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1
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1, 1, 2, 2, 3, 6, 5, 8, 9, 13, 12, 23, 18, 27, 33, 39, 38, 63, 54, 80, 86, 101, 104, 161, 145, 183, 208, 254, 256, 361, 340, 435, 472, 550, 600, 776, 760, 918, 1018, 1221, 1260, 1576, 1610, 1929, 2129, 2408, 2590, 3172, 3274, 3833, 4173, 4783, 5120, 6054, 6414, 7414, 8025
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OFFSET
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1,3
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COMMENTS
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Number of ways to write n as an orderless product of orderless sums with distinct factors and each sum composed of distinct parts. Compare A318949.
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LINKS
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EXAMPLE
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The a(4) = 2 ways: (4), (3+1).
The a(6) = 6 ways: (6), (4+2), (5+1), (3+2+1), (2)*(3), (2)*(2+1).
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PROG
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(PARI)
MultWeighT(u)={my(n=#u, v=vector(n, k, k==1)); for(k=2, n, if(u[k], my(m=logint(n, k), p=(1 + x + O(x*x^m))^u[k], w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w))); v}
seq(n)={MultWeighT(Vec(eta(x^2 + O(x*x^n))/eta(x + O(x*x^n)) - 1))} \\ Andrew Howroyd, Oct 27 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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