OFFSET
1,2
LINKS
Seiichi Manyama, Antidiagonals n = 1..52, flattened
Mathematics.StackExchange, Find the number of k 1's, k 2's, ... , k n's - total kn cards, Apr 08 2012.
FORMULA
A(n,k) = k! * A322013(n,k).
Let q_n(x) = Sum_{i=1..n} (-1)^(n-i) * binomial(n-1, n-i) * x^i/i!.
A(n,k) = Integral_{0..infinity} (q_n(x))^k * exp(-x) dx.
EXAMPLE
Square array begins:
1, 2, 6, 24, 120, 720, ...
0, 2, 30, 864, 39480, 2631600, ...
0, 2, 174, 41304, 19606320, 16438575600, ...
0, 2, 1092, 2265024, 11804626080, 131402141197200, ...
0, 2, 7188, 134631576, 7946203275000, 1210527140790855600, ...
PROG
(PARI)
q(n, x) = sum(i=1, n, (-1)^(n-i) * binomial(n-1, n-i) * x^i/i!)
T(n, k) = subst(serlaplace(q(n, x)^k), x, 1) \\ Andrew Howroyd, Feb 03 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 26 2018
STATUS
approved