OFFSET
0,8
FORMULA
G.f. of column k: Sum_{j>=0} (k*x)^j/(1 - j*x).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 6, 12, 20, 30, 42, ...
0, 4, 18, 48, 100, 180, 294, ...
0, 9, 58, 201, 516, 1105, 2094, ...
0, 23, 202, 885, 2756, 6955, 15198, ...
0, 66, 762, 4116, 15300, 45030, 112686, ...
MATHEMATICA
T[0, k_] := 1; T[n_, 0] = 0; T[n_, k_] := Sum[k^j * j^(n - j), {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 08 2022 *)
PROG
(PARI) T(n, k) = sum(j=0, n, k^j*j^(n-j));
CROSSREFS
KEYWORD
AUTHOR
Seiichi Manyama, Feb 08 2022
STATUS
approved