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%I #15 Nov 16 2023 05:17:27
%S 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,
%T 66,13,1,36,210,462,495,286,91,15,1,45,330,924,1287,1001,455,120,17,1,
%U 55,495,1716,3003,3003,1820,680,153,19,1,66,715,3003,6435,8008,6188,3060
%N Number of pairwise disjoint unions of m integer-to-integer subintervals of [0,n]; a rectangular array by antidiagonals, n>=2m-1, m>=1.
%C Main diagonal: A025174.
%H Reinhard Zumkeller, <a href="/A143858/b143858.txt">Rows n = 1..125 of triangle, flattened</a>
%F 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.
%e 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].
%e 1 3 6 10 15 21 28 36 45 55 66 78
%e 0 0 1 5 15 35 70 126 210 330 495 715
%e 0 0 0 0 1 7 28 84 210 462 924 1716
%e 0 0 0 0 0 0 1 9 45 165 495 1287
%e 0 0 0 0 0 0 0 0 1 11 66 286
%e 0 0 0 0 0 0 0 0 0 0 1 13
%p A143858 := proc(m,n)
%p binomial(n-1+2*m,2*m) ;
%p end proc:
%p seq(seq( A143858(n,d-n),n=1..d-1),d=2..8) ; # _R. J. Mathar_, Nov 16 2023
%o (Haskell) Seen as a triangle read by rows
%o a143858 n k = a143858_tabl !! (n-1) !! k
%o a143858_row n = a143858_tabl !! (n-1)
%o a143858_tabl = map ((++ [1]) . tail) a258993_tabl
%o -- _Reinhard Zumkeller_, Jun 22 2015
%Y Cf. A007318, A025174, A109954, A085478, A258993.
%K nonn,tabf,easy
%O 1,2
%A _Clark Kimberling_, Sep 03 2008
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