OFFSET
1,8
COMMENTS
Triangle T(n,k)*(2*k)!/(n+k)!)=
1. Riordan Array (1,(2-2*cos(x))/x) without first column.
2. Riordan Array ((2-2*cos(x))/x^2,(2-2*cos(x))/x) numbering triangle (0,0).
FORMULA
T(n,k):=((-1)^k*2^k*((-1)^(n+k)+1)*sum(j=1..k, ((sum(i=0..(j-1)/2, (j-2*i)^(n+k)*binomial(j,i))) *binomial(k,j)*(-1)^((n+k)/2+k-j))/2^j))/(2*k)!
EXAMPLE
1
0, 1
-1, 0, 1
0, -5, 0, 1
1, 0, -14, 0, 1
0, 21, 0, -30, 0, 1
-1, 0, 147, 0, -55, 0, 1
PROG
(Maxima)
T(n, k):=((-1)^k*2^k*((-1)^(n+k)+1)*sum(((sum((j-2*i)^(n+k)*binomial(j, i), i, 0, (j-1)/2))*binomial(k, j)*(-1)^((n+k)/2+k-j))/2^j, j, 1, k))/(2*k)!
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Vladimir Kruchinin, Nov 11 2011
STATUS
approved