OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..150, flattened
FORMULA
The mixed e.g.f./o.g.f. is Sum_{k=0..n} T(n, k)*x^n/n!*y^k = (sec(x) + tan(x))*sec(xy)*(sec(xy) + tan(xy)).
EXAMPLE
Table begins
\ k..0....1....2....3....4....
n
0 |..1
1 |..1....1
2 |..1....2....2
3 |..2....3....6....5
4 |..5....8...12...20...16
5 |.16...25...40...50...80...61
6 |.61...96..150..200..240..366..272
For example, a(3,1) counts 45132, 35142, 25143---the alternating permutations on [5] with 5 preceding 1 and 1 in position 3.
MAPLE
b:= proc(u, o) option remember; `if`(u+o=0, 1,
add(b(o-1+j, u-j), j=1..u))
end:
T:= (n, k)-> binomial(n, k)*b(k+1, 0)*b(n-k, 0):
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Apr 25 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Callan, Mar 02 2005
STATUS
approved