OFFSET
0,5
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
N. J. A. Sloane, Transforms
FORMULA
E.g.f. of column k: exp(x) * (-LambertW(-x)/x)^k.
A(n,k) = Sum_{j=0..n} k * (n-j+k)^(n-j-1) * C(n,j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, ...
1, 6, 13, 22, 33, 46, 61, ...
1, 29, 81, 163, 281, 441, 649, ...
1, 212, 689, 1564, 2993, 5156, 8257, ...
1, 2117, 7553, 18679, 38705, 71801, 123217, ...
1, 26830, 101961, 268714, 592489, 1166886, 2120545, ...
MAPLE
hymtr:= proc(p) proc(n, m) `if`(m=0, p(n), m*add(
p(k)*binomial(n, k) *(n-k+m)^(n-k-1), k=0..n))
end end:
A:= hymtr(1):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
a[_, 0] = 1; a[n_, k_] := Sum[k*(n - j + k)^(n - j - 1)*Binomial[n, j], {j, 0, n}]; Table[a[n - k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Jun 24 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 17 2008, revised Oct 30 2012
STATUS
approved