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A327843
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Number of colored integer partitions of 2n using all colors of an n-set such that a color pattern for part i has i distinct colors in increasing order.
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2
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1, 1, 7, 94, 2081, 67390, 2969647, 169299808, 12032189630, 1036485156029, 105880393642170, 12604896326749405, 1724189631362670619, 267831346979691504798, 46782781937811822181581, 9111872329195713764645644, 1964607669245374038857479576
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 7: 2ab2ab, 2ab1a1a, 2ab1a1b, 2ab1b1b 1a1a1a1b, 1a1a1b1b, 1a1b1b1b.
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, min(n-i*j, i-1), k)*binomial(
binomial(k, i)+j-1, j), j=0..n/i)))
end:
a:= n-> add(b(2*n$2, i)*(-1)^(n-i)*binomial(n, i), i=0..n):
seq(a(n), n=0..17);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[b[n - i*j, Min[n - i*j, i - 1], k] Binomial[Binomial[k, i] + j - 1, j], {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, i] (-1)^(n-i) Binomial[n, i], {i, 0, n}];
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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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