OFFSET
1,14
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
EXAMPLE
: T(6,4) = 3 : T(11,3) = 1 :
: o o o : o :
: / \ | | : /( )\ :
: o o o o : o o o o :
: | / \ | : /| | | :
: o o o o : o o o o :
: | | / \ : | | :
: o o o o : o o :
: | | | : :
: o o o : :
Triangle T(n,k) begins:
1;
0, 1;
0, 0, 1;
0, 0, 1, 1;
0, 0, 0, 2, 1;
0, 0, 0, 2, 3, 1;
0, 0, 0, 2, 5, 4, 1;
0, 0, 0, 2, 8, 9, 5, 1;
0, 0, 0, 1, 12, 18, 14, 6, 1;
0, 0, 0, 1, 17, 34, 33, 20, 7, 1;
0, 0, 0, 1, 23, 61, 72, 54, 27, 8, 1;
0, 0, 0, 0, 32, 108, 149, 132, 82, 35, 9, 1;
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1 or k<1, 0,
add(binomial(b((i-1)$2, k-1), j)*b(n-i*j, i-1, k), j=0..n/i)))
end:
T:= (n, k)-> b((n-1)$2, k) -`if`(k=0, 0, b((n-1)$2, k-1)):
seq(seq(T(n, k), k=0..n-1), n=1..15);
MATHEMATICA
Drop[Transpose[Map[PadRight[#, 15]&, Table[f[n_]:=Nest[ CoefficientList[ Series[ Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 15}], x]&, {1}, n]; f[m]-PadRight[f[m-1], Length[f[m]]], {m, 1, 15}]]], 1]//Grid (* Geoffrey Critzer, Aug 01 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 31 2013
STATUS
approved