cp's OEIS Frontend

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.

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