OFFSET
0,5
COMMENTS
FORMULA
T(n, k) = A101981(n-k)*C(n, k)^2.
EXAMPLE
Rows begin:
[0],
[1,0],
[ -1,4,0],
[4,-9,9,0],
[ -33,64,-36,16,0],
[456,-825,400,-100,25,0],
[ -9460,16416,-7425,1600,-225,36,0],
[274800,-463540,201096,-40425,4900,-441,49,0],
[ -10643745,17587200,-7416640,1430016,-161700,12544,-784,64,0],...
and equal the term-by-term product of column 0:
A101981 = {0,1,-1,4,-33,456,-9460,274800,-10643745,...}
with the rows of the squared Pascal's triangle (A008459):
[0],
[1*1^2, 0*1^2],
[ -1*1^2, 1*2^2, 0*1^2],
[4*1^2, -1*3^2, 1*3^2, 0*1^2],
[ -33*1^2, 4*4^2, -1*6^2, 1*4^2, 0*1^2],
[456*1^2, -33*5^2, 4*10^2, -1*10^2, 1*5^2, 0*1^2],...
PROG
(PARI) {T(n, k)=if(n<k||k<0, 0, sum(m=1, n, (-1)^(m-1)* (matrix(n+1, n+1, i, j, if(i>j, binomial(i-1, j-1)^2))^m/m)[n+1, k+1]))}
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Dec 23 2004
STATUS
approved