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A327881
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Number of set partitions of [n] with distinct block sizes and one of the block sizes is 2.
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2
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0, 0, 1, 3, 0, 10, 75, 126, 196, 1548, 15525, 39820, 161106, 358722, 3705884, 46623045, 142988280, 768721504, 3560215293, 12250746432, 144581799790, 2542575063630, 8955836934660, 55657973021431, 319349051391228, 1983548989621200, 7898257536096850
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OFFSET
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0,4
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COMMENTS
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Sum of multinomials M(n; lambda), where lambda ranges over all integer partitions of n into distinct parts and one part is 2.
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LINKS
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EXAMPLE
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a(2) = 1: 12.
a(3) = 3: 12|3, 13|2, 1|23.
a(4) = 0.
a(5) = 10: 123|45, 124|35, 125|34, 12|345, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234.
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MAPLE
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b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, `if`(i<2, 0, b(n, i-1, `if`(i=k, 0, k)))+
`if`(i=k, 0, b(n-i, min(n-i, i-1), k)*binomial(n, i))))
end:
a:= n-> b(n$2, 0)-b(n$2, 2):
seq(a(n), n=0..29);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k] Binomial[n, i]]]];
a[n_] := b[n, n, 0] - b[n, n, 2];
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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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