OFFSET
0,3
FORMULA
n*T(n,k) = 3 * Sum_{j=0..k} binomial(k,j)*(3*n-2-2*j)*T(n-1-j,k) for n > k.
T(n,k) = Sum_{j=0..n} (-9)^j * binomial(-1/3,j) * binomial(k*j,n-j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
3, 3, 3, 3, 3, 3, ...
18, 21, 24, 27, 30, 33, ...
126, 162, 201, 243, 288, 336, ...
945, 1341, 1809, 2352, 2973, 3675, ...
7371, 11529, 16893, 23607, 31818, 41676, ...
PROG
(PARI) T(n, k) = sum(j=0, n, (-9)^j*binomial(-1/3, j)*binomial(k*j, n-j));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved