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A143858 Number of pairwise disjoint unions of m integer-to-integer subintervals of [0,n]; a rectangular array by antidiagonals, n>=2m-1, m>=1. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Main diagonal: A025174.
LINKS
FORMULA
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.
EXAMPLE
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
MAPLE
A143858 := proc(m, n)
binomial(n-1+2*m, 2*m) ;
end proc:
seq(seq( A143858(n, d-n), n=1..d-1), d=2..8) ; # R. J. Mathar, Nov 16 2023
PROG
(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
-- Reinhard Zumkeller, Jun 22 2015
CROSSREFS
Sequence in context: A208331 A061702 A112351 * A258993 A109954 A355010
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Sep 03 2008
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)