OFFSET
0,8
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
T(0,k) = 1, T(1,k) = k; 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.
G.f. of column k: (1 - k * x)/(1 - 2 * k * x + (k-1) * k * x^2).
E.g.f. of column k: exp(k * x) * cosh(sqrt(k) * x).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 2, 6, 12, 20, 30, ...
0, 4, 20, 54, 112, 200, ...
0, 8, 68, 252, 656, 1400, ...
0, 16, 232, 1188, 3904, 10000, ...
PROG
(PARI) T(n, k) = sum(j=0, n\2, k^(n-j)*binomial(n, 2*j));
(PARI) T(n, k) = round(((k+sqrt(k))^n+(k-sqrt(k))^n))/2;
CROSSREFS
KEYWORD
AUTHOR
Seiichi Manyama, Mar 11 2023
STATUS
approved