OFFSET
0,9
FORMULA
T(0,k) = 0, T(1,k) = 1; T(n,k) = 2 * k * T(n-1,k) - (k-1) * k * T(n-2,k).
T(n,k) = ((k + sqrt(k))^n - (k - sqrt(k))^n)/(2 * sqrt(k)) for k > 0.
G.f. of column k: x/(1 - 2 * k * x + (k-1) * k * x^2).
E.g.f. of column k: exp(k * x) * sinh(sqrt(k) * x) / sqrt(k) for k > 0.
EXAMPLE
Square array begins:
0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1 , 1, ...
0, 2, 4, 6, 8, 10, ...
0, 4, 14, 30, 52, 80, ...
0, 8, 48, 144, 320, 600, ...
0, 16, 164, 684, 1936, 4400, ...
PROG
(PARI) T(n, k) = polcoef(lift(Mod('x, ('x-k)^2-k)^n), 1);
CROSSREFS
KEYWORD
AUTHOR
Seiichi Manyama, Mar 11 2023
STATUS
approved