OFFSET
0,25
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
E.g.f. of column k: exp(Sum_{d|k, d>1} x^d/d).
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 1, 0, 1, 0, 1, 0, 1, ...
0, 0, 0, 2, 0, 0, 2, 0, 0, ...
0, 0, 3, 0, 9, 0, 3, 0, 9, ...
0, 0, 0, 0, 0, 24, 20, 0, 0, ...
0, 0, 15, 40, 105, 0, 175, 0, 105, ...
0, 0, 0, 0, 0, 0, 210, 720, 0, ...
0, 0, 105, 0, 2625, 0, 4585, 0, 7665, ...
MAPLE
with(numtheory):
A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(mul(n-i, i=1..j-1)*A(n-j, k), j=divisors(k) minus {1})))
end:
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
A[0, 0] = A[0, 1] = 1; A[_, 0|1] = 0; A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n - i, {i, 1, j - 1}]*A[n - j, k], {j, Rest @ Divisors[k]}]]]; Table[A[n, d - n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jan 21 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 18 2015
STATUS
approved