OFFSET
0,6
LINKS
FORMULA
T(n,k) = Sum_{i=0..k} (-1)^i * C(k,i) * A246106(n,k-i).
EXAMPLE
T(2,2) = 5:
[1 1] [1 2] [1 2] [1 1] [1 2]
[1 2] [2 2] [1 2] [2 2] [2 1].
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 5;
0, 1, 34, 633;
0, 1, 315, 89544, 7520386;
0, 1, 5622, 64780113, 79587235420, 20435529209470;
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [[]],
`if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
b(n-i*j, i-1))[], j=1..n/i)]))
end:
A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*
igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
/mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2))
end:
T:= (n, k)-> add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k):
seq(seq(T(n, k), k=0..n), n=0..8);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 13 2015
STATUS
approved