OFFSET
1,2
COMMENTS
Row sums = A108958: (1, 6, 27, 110, 430, 1652, ...).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
T(n,k) = A065420(n-1,k-1)/2. - R. J. Mathar, Apr 04 2012
EXAMPLE
Row 4 of Pascal's triangle (1, 4, 6, 4, 1) with each term squared = (1, 16, 36, 16, 1), then subtracting (1, 4, 6, 4, 1) = (0, 12, 30, 12, 0). Dividing by 2 and deleting the zeros, we get row 4 of A143418: (6, 15, 6).
First few rows of the triangle =
1;
3, 3;
6, 15, 6;
10, 45, 45, 10;
15, 105, 190, 105, 15;
21, 210, 595, 595, 210, 21;
28, 378, 1540, 2415, 1540, 378, 28;
...
MAPLE
A143418 := proc(n, k)
binomial(n, k)*(binomial(n, k)-1)/2 ;
end proc:
seq(seq(A143418(n, k), k=1..n-1), n=1..12) ; # R. J. Mathar, Apr 04 2012
MATHEMATICA
Table[Binomial[n, k] (Binomial[n, k]-1)/2, {n, 20}, {k, n-1}]//Flatten (* Harvey P. Dale, Jun 14 2021 *)
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson and Roger L. Bagula, Aug 14 2008
EXTENSIONS
Corrected by Harvey P. Dale, Jun 14 2021
STATUS
approved