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A266693
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Number of partitions of n with product of multiplicities of parts equal to 10.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 4, 2, 7, 8, 12, 13, 19, 22, 32, 36, 46, 64, 72, 88, 112, 134, 160, 203, 236, 287, 343, 412, 477, 577, 676, 798, 944, 1101, 1283, 1516, 1754, 2030, 2361, 2738, 3157, 3657, 4202, 4826, 5567, 6356, 7279, 8340, 9494, 10815
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OFFSET
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0,13
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LINKS
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FORMULA
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a(n) ~ c * exp(Pi*sqrt(n/3)) * n^(1/4), where c = 0.007782666499... - Vaclav Kotesovec, May 24 2018
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EXAMPLE
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a(9) = 1: [1,1,1,1,1,2,2].
a(12) = 3: [1,1,1,1,1,1,1,1,1,1,2], [1,1,2,2,2,2,2], [1,1,1,1,1,2,2,3].
a(13) = 4: [1,1,1,1,1,1,1,1,1,1,3], [1,1,1,1,1,2,3,3], [1,1,1,1,1,2,2,4], [1,1,1,1,1,4,4].
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MAPLE
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b:= proc(n, i, p) option remember; `if`(i*(p+(i-1)/2)<n, 0, `if`(n=0,
`if`(p=1, 1, 0), b(n, i-1, p) +add(`if`(irem(p, j)>0, 0, (h->
b(h, min(h, i-1), p/j))(n-i*j)), j=1..min(p, n/i))))
end:
a:= b(n$2, 10):
seq(a(n), n=0..65);
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[i*(p + (i - 1)/2) < n, 0, If[n == 0, If[p == 1, 1, 0], b[n, i - 1, p] + Sum[If[Mod[p, j] > 0, 0, Function[h, b[h, Min[h, i - 1], p/j]][n - i*j]], {j, 1, Min[p, n/i]}]]];
a[n_] := b[n, n, 10];
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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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