OFFSET
0,8
COMMENTS
Row sums are 1,1,1,1,1,1 with g.f. 1/(1-x). Can also be obtained from triangle A080232 by taking sums of pairs of consecutive row elements.
Mirror image of triangle in A156644. - Philippe Deléham, Feb 14 2009
FORMULA
T(n, k) = if(k>n, 0, binomial(n, k)-binomial(n, k-1)).
EXAMPLE
Rows are {1}, {1,0}, {1,1,-1}, {1,2,0,-2}, {1,3,2,-2,-3}, ...
MATHEMATICA
Table[Binomial[n, k] - Binomial[n, k - 1], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)
PROG
(PARI) {T(n, k) = if( n<0 || k>n, 0, binomial(n, k) - binomial(n, k-1))}; /* Michael Somos, Nov 25 2016 */
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 10 2003
STATUS
approved