OFFSET
0,9
LINKS
OEIS Wiki, Eulerian polynomials.
FORMULA
G.f. of column k: x*A_k(x)/((1-k*x) * (1-x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.
T(0,k) = 0^k; T(n,k) = k*T(n-1,k) + n^k.
EXAMPLE
Square array begins:
1, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 3, 6, 11, 20, 37, 70, ...
1, 6, 21, 60, 161, 428, 1149, ...
1, 10, 58, 244, 900, 3164, 10990, ...
1, 15, 141, 857, 4225, 18945, 81565, ...
1, 21, 318, 2787, 18196, 102501, 536046, ...
PROG
(PARI) T(n, k) = sum(j=0, n, k^(n-j)*j^k);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Dec 27 2023
STATUS
approved