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A143858
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Number of pairwise disjoint unions of m integer-to-integer subintervals of [0,n]; a rectangular array by antidiagonals, n>=2m-1, m>=1.
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6
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1, 3, 1, 6, 5, 1, 10, 15, 7, 1, 15, 35, 28, 9, 1, 21, 70, 84, 45, 11, 1, 28, 126, 210, 165, 66, 13, 1, 36, 210, 462, 495, 286, 91, 15, 1, 45, 330, 924, 1287, 1001, 455, 120, 17, 1, 55, 495, 1716, 3003, 3003, 1820, 680, 153, 19, 1, 66, 715, 3003, 6435, 8008, 6188, 3060
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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R(m,n) = C(n+1,2m), where n>=2m-1, m>=1. R is also given by the absolute values of terms in A109954.
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EXAMPLE
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R(2,4) counts these unions of 2 subintervals of [0,4]: [0,1]U[2,3], [0,1]U[2,4], [0,1]U[3,4], [0,2]U[3,4], [1,2]U[3,4].
1 3 6 10 15 21 28 36 45 55 66 78
0 0 1 5 15 35 70 126 210 330 495 715
0 0 0 0 1 7 28 84 210 462 924 1716
0 0 0 0 0 0 1 9 45 165 495 1287
0 0 0 0 0 0 0 0 1 11 66 286
0 0 0 0 0 0 0 0 0 0 1 13
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MAPLE
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binomial(n-1+2*m, 2*m) ;
end proc:
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PROG
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(Haskell) Seen as a triangle read by rows
a143858 n k = a143858_tabl !! (n-1) !! k
a143858_row n = a143858_tabl !! (n-1)
a143858_tabl = map ((++ [1]) . tail) a258993_tabl
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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