OFFSET
0,13
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
A(n,k) = Sum_{i=0..min(n,k)} A226874(n,i).
EXAMPLE
A(4,3) = 23: aaaa, aaab, aaba, aabb, aabc, aacb, abaa, abab, abac, abba, abca, acab, acba, baaa, baab, baac, baba, baca, bbaa, bcaa, caab, caba, cbaa.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 3, 3, 3, 3, 3, 3, ...
0, 1, 4, 10, 10, 10, 10, 10, ...
0, 1, 11, 23, 47, 47, 47, 47, ...
0, 1, 16, 66, 126, 246, 246, 246, ...
0, 1, 42, 222, 522, 882, 1602, 1602, ...
0, 1, 64, 561, 1821, 3921, 6441, 11481, ...
MAPLE
b:= proc(n, i, t) option remember;
`if`(t=1, 1/n!, add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
A:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[t == 1, 1/n!, Sum[b[n-j, j, t-1]/j!, {j, i, n/t}]]; a[n_, k_] := If[k == 0, If[n == 0, 1, 0], n!*b[n, 0, k]]; Table[Table[a[n, d-n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Dec 13 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 21 2013
STATUS
approved