OFFSET
1,3
LINKS
Seiichi Manyama, Antidiagonals n = 1..140, flattened
FORMULA
G.f. of column k: (1/(1 - x)) * Sum_{j>=1} (j^k - (j - 1)^k) * x^j/(1 - x^j)^2.
T(n,k) = Sum_{j=1..n} j * Sum_{d|j} (d^k - (d - 1)^k)/d.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
4, 6, 10, 18, 34, 66, 130, ...
8, 14, 32, 86, 248, 734, 2192, ...
15, 31, 87, 295, 1095, 4231, 16647, ...
21, 45, 153, 669, 3201, 15765, 78393, ...
33, 81, 309, 1521, 8373, 48321, 284709, ...
41, 101, 443, 2633, 17411, 119321, 828323, ...
MATHEMATICA
T[n_, k_] := Sum[j * Floor[n/j]^k, {j, 1, n}]; Table[T[k, n - k + 1], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 14 2021 *)
PROG
(PARI) T(n, k) = sum(j=1, n, j*(n\j)^k);
(PARI) T(n, k) = sum(j=1, n, j*sumdiv(j, d, (d^k-(d-1)^k)/d));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Dec 14 2021
STATUS
approved