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A026835
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Triangular array read by rows: T(n,k) = number of partitions of n into distinct parts in which every part is >=k, for k=1,2,...,n.
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7
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1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 4, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 6, 3, 2, 1, 1, 1, 1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 1, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1, 12, 7, 4, 3, 2, 1, 1, 1, 1, 1, 1, 15, 8, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 18, 10, 6, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 22, 12, 7, 4, 3, 2, 1, 1
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (y^k*(-1+Product_{i>=k} (1+x^i))). - Vladeta Jovovic, Aug 25 2003
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EXAMPLE
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Table begins:
1
1 1
2 1 1
2 1 1 1
3 2 1 1 1
4 2 1 1 1 1
5 3 2 1 1 1 1
6 3 2 1 1 1 1 1
8 5 3 2 1 1 1 1 1
10 5 3 2 1 1 1 1 1 1
12 7 4 3 2 1 1 1 1 1 1
15 8 5 3 2 1 1 1 1 1 1 1
... (End)
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MATHEMATICA
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Nest[Function[{T, n, r}, Append[T, Table[1 + Total[T[[##]] & @@@ Select[r, #[[-1]] > k + 1 &]], {k, 0, n}]]] @@ {#1, #2, Transpose[1 + {#2 - #3, #3}]} & @@ {#1, #2, Range[Ceiling[#2/2] - 1]} & @@ {#, Length@ #} &, {{1}}, 12] // Flatten (* Michael De Vlieger, Aug 03 2020 *)
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PROG
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(Haskell)
import Data.List (tails)
a026835 n k = a026835_tabl !! (n-1) !! (k-1)
a026835_row n = a026835_tabl !! (n-1)
a026835_tabl = map
(\row -> map (p $ last row) $ init $ tails row) a002260_tabl
where p 0 _ = 1
p _ [] = 0
p m (k:ks) = if m < k then 0 else p (m - k) ks + p m ks
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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