OFFSET
0,2
FORMULA
Sum_{k, 0<=k<=n} T(n,k)*x^k = A005043(n), A001006(n), A005773(n+1), A059738(n) for x = -2, -1, 0, 1 respectively.
T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-1)^i. - Philippe Deléham, Feb 23 2012
T(n,k) = (k+1)*Sum_{j=0..n-k} C(2*j+k,j)*(-1)^j*3^(n-j-k)*C(n+1,j+k+1)/(n+1). - Vladimir Kruchinin Sep 30 2020
EXAMPLE
Triangle T(n,k) (0<=k<=n) begins:
1;
2, 1;
5, 4, 1;
13, 14, 6, 1;
35, 46, 27, 8, 1;
96, 147, 107, 44, 10, 1;
...
PROG
(Maxima)
T(n, k)=((k+1)*sum(binomial(2*j+k, j)*(-1)^j*3^(n-j-k)*binomial(n+1, j+k+1), j, 0, n-k))/(n+1); /* Vladimir Kruchinin Sep 30 2020 */
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Dec 10 2009
STATUS
approved