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A090824
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Triangle read by rows: T(n,k) = number of partitions of binomial(n,k) into parts greater than k and not greater than n, 0<=k<=n.
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2
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0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 4, 7, 4, 1, 1, 0, 1, 4, 20, 19, 5, 1, 1, 0, 1, 7, 67, 159, 57, 8, 1, 1, 0, 1, 8, 238, 1607, 1163, 157, 9, 1, 1, 0, 1, 12, 868, 20478, 37251, 7546, 387, 13, 1, 1, 0, 1, 14, 3311, 312511, 1749868, 688733, 41377, 895, 16, 1, 1, 0
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OFFSET
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0,12
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COMMENTS
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n>0: T(n,0) = 1, T(n,1) = A002865(n);
T(n,n-2) = 1 for n>1; T(n,n-1) = 1 for n>0; T(n,n) = 0.
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LINKS
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EXAMPLE
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T(6,2) = #{partitions of binomial(6,2)=15 into parts i with 2<i<=6}
= #{6+6+3, 6+5+4, 6+3+3+3, 5+5+5, 5+4+3+3, 4+4+4+3, 3+3+3+3+3} = 7;
T(6,3) = #{partitions of binomial(6,3)=20 into parts i with 3<i<=6}
= #{6+6+4+4, 6+5+5+4, 5+5+5+5, 4+4+4++4+4} = 4.
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PROG
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(Haskell)
a090824 n k = a090824_tabl !! n !! k
a090824_row n = a090824_tabl !! n
a090824_tabl = zipWith (zipWith p)
(map (\x -> map (`enumFromTo` x) [1..x+1]) [0..]) a007318_tabl
where p _ 0 = 1
p [] _ = 0
p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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