OFFSET
0,9
LINKS
Alois P. Heinz, Rows n = 0..30, flattened
EXAMPLE
The 5 partitions of n=4 are 1+1+1+1 (lcm=1), 1+1+2 (lcm=2), 2+2 (lcm=2), 1+3 (lcm=3) and 4 (lcm=4). So k=1, 3 and 4 appear once, k=2 appears twice.
The triangle starts:
1 ;
1 ;
1 1;
1 1 1;
1 2 1 1;
1 2 1 1 1 1;
1 3 2 2 1 2;
1 3 2 2 1 3 1 0 0 1 0 1;
...
MAPLE
A256067 := proc(n, k)
local a, p ;
a := 0 ;
for p in combinat[partition](n) do
ilcm(op(p)) ;
if % = k then
a := a+1 ;
end if;
end do:
a;
end proc:
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0 or i=1, x,
b(n, i-1)+(p-> add(coeff(p, x, t)*x^ilcm(t, i),
t=1..degree(p)))(add(b(n-i*j, i-1), j=1..n/i)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n$2)):
seq(T(n), n=0..12); # Alois P. Heinz, Mar 27 2015
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, x, b[n, i-1] + Function[{p}, Sum[ Coefficient[p, x, t]*x^LCM[t, i], {t, 1, Exponent[p, x]}]][Sum[b[n-i*j, i-1], {j, 1, n/i}]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Jun 22 2015, after Alois P. Heinz *)
CROSSREFS
Cf. A000041 (row sums), A000793 (row lengths), A213952, A074761 (diagonal), A074752 (6th column), A008642 (4th column), A002266 (5th column), A002264 (3rd column), A132270 (7th column), A008643 (8th column), A008649 (9th column), A258470 (10th column).
KEYWORD
nonn,tabf
AUTHOR
R. J. Mathar, Mar 18 2015
EXTENSIONS
T(0,1)=1 prepended by Alois P. Heinz, Mar 27 2015
STATUS
approved