OFFSET
0,6
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
T(n,k) = Sum_{i=0..k} (-1)^i * A213028(n,k-i) / (i!*(k-i)!).
EXAMPLE
T(0,0) = 1: (the empty word).
T(1,1) = 1: aaa.
T(2,1) = 1: aaaaaa.
T(2,2) = 3: aaabbb, aabbba, abbbaa.
T(3,1) = 1: aaaaaaaaa.
T(3,2) = 18: aaaaaabbb, aaaaabbba, aaaabbbaa, aaabaaabb, aaabbaaab, aaabbbaaa, aaabbbbbb, aabaaabba, aabbaaaba, aabbbaaaa, aabbbabbb, aabbbbbba, abaaabbaa, abbaaabaa, abbbaaaaa, abbbaabbb, abbbabbba, abbbbbbaa.
T(3,3) = 12: aaabbbccc, aaabbcccb, aaabcccbb, aabbbaccc, aabbbccca, aabbcccba, aabcccbba, abbbaaccc, abbbaccca, abbbcccaa, abbcccbaa, abcccbbaa.
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 3;
0, 1, 18, 12;
0, 1, 97, 198, 55;
0, 1, 530, 2520, 1820, 273;
0, 1, 2973, 29886, 42228, 15300, 1428;
0, 1, 17059, 347907, 859180, 564585, 122094, 7752;
MAPLE
A:= (n, k)-> `if`(n=0, 1,
k/n *add(binomial(3*n, j) *(n-j) *(k-1)^j, j=0..n-1)):
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
seq(seq(T(n, k), k=0..n), n=0..10);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 25 2015
STATUS
approved