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A370358
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Number of partitions of [3n] into n sets of size 3 having at least one set {3j-2,3j-1,3j} (1<=j<=n).
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4
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0, 1, 1, 28, 1063, 74296, 8182855, 1305232804, 284438292607, 81167321350432, 29367491879327959, 13135455977606994340, 7116140280642196449151, 4591529352468711908776288, 3479040085783649820897765223, 3058744793640846605215609362436
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n-1} (-1)^(n-j+1) * binomial(n,j) * A025035(j).
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EXAMPLE
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a(1) = 1: 123.
a(2) = 1: 123|456.
a(3) = 28: 123|456|789, 123|457|689, 123|458|679, 123|459|678, 123|467|589, 123|468|579, 123|469|578, 123|478|569, 123|479|568, 123|489|567, 124|356|789, 125|346|789, 126|345|789, 127|389|456, 128|379|456, 129|378|456, 134|256|789, 135|246|789, 136|245|789, 137|289|456, 138|279|456, 139|278|456, 145|236|789, 146|235|789, 156|234|789, 178|239|456, 179|238|456, 189|237|456.
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MAPLE
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b:= proc(n) option remember; `if`(n<3, [1, 0, 9][n+1],
9*(n*(n-1)/2*b(n-1)+(n-1)^2*b(n-2)+(n-1)*(n-2)/2*b(n-3)))
end:
a:= n-> (3*n)!/(n!*(3!)^n)-b(n):
seq(a(n), n=0..20);
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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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