A357882 - OEIS

A357882

Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* |Stirling1(n,k*j)|/j!.

1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 2, 6, 0, 1, 0, 0, 6, 24, 0, 1, 0, 0, 6, 34, 120, 0, 1, 0, 0, 0, 36, 220, 720, 0, 1, 0, 0, 0, 24, 210, 1688, 5040, 0, 1, 0, 0, 0, 0, 240, 1710, 14868, 40320, 0, 1, 0, 0, 0, 0, 120, 2040, 17304, 147684, 362880, 0, 1, 0, 0, 0, 0, 0, 1800, 17640, 194712, 1631376, 3628800, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,9

LINKS

Table of n, a(n) for n=0..77.

FORMULA

For k > 0, e.g.f. of column k: exp((-log(1-x))^k).

T(0,k) = 1; T(n,k) = k! * Sum_{j=1..n} binomial(n-1,j-1) * |Stirling1(j,k)| * T(n-j,k).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, ...

0, 1, 0, 0, 0, 0, ...