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.

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

Offset

1,2

Comments

Main diagonal: A025174.

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

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

Cf. A007318, A025174, A109954, A085478, A258993.

Sequence in context: A208331 A061702 A112351 * A258993 A109954 A355010

Adjacent sequences: A143855 A143856 A143857 * A143859 A143860 A143861

Keyword

nonn,tabf,easy

Author

Clark Kimberling, Sep 03 2008

Status

approved