OFFSET
0,5
COMMENTS
For r > 1, row r is asymptotic to sqrt(2*Pi) * (r*n)^(r*n + 1/2) / ((r!)^n * exp(r*n-1)). - Vaclav Kotesovec, May 24 2020
LINKS
Seiichi Manyama, Antidiagonals n = 0..50, flattened
FORMULA
A(n,k) = Sum_{i=0..k*n} b(i) where Sum_{i=0..k*n} b(i) * x^i/i! = (Sum_{i=0..n} x^i/i!)^k.
EXAMPLE
For (n,k) = (3,2), (Sum_{i=0..3} x^i/i!)^2 = (1 + x + x^2/2 + x^3/6)^2 = 1 + 2*x + 4*x^2/2 + 8*x^3/6 + 14*x^4/24 + 20*x^5/120 + 20*x^6/720. So A(3,2) = 1 + 2 + 4 + 8 + 14 + 20 + 20 = 69.
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 5, 16, 65, 326, ...
1, 3, 19, 271, 7365, 326011, ...
1, 4, 69, 5248, 1107697, 492911196, ...
1, 5, 251, 110251, 191448941, 904434761801, ...
1, 6, 923, 2435200, 35899051101, 1856296498826906, ...
1, 7, 3431, 55621567, 7101534312685, 4098746255797339511, ...
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 19 2019
STATUS
approved