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
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Sep 03 2008
STATUS
approved