OFFSET
1,16
COMMENTS
FORMULA
T(n, k) = T(n-k, k+1) + ... + T(n-k, n-k) for 1<=k<=m and T(n, k)=0 for m+1<=k<=n-1, where m=[ (n-1)/2 ]; T(n, n)=1 for n >= 1.
G.f.: sum(t^j*x^j*product(1+x^i,i=j+1..infinity),j=1..infinity). - Emeric Deutsch, Feb 24 2006
EXAMPLE
T(11,2)=3 because we have [9,2],[6,3,2] and [5,4,2].
Triangle starts:
1;
0,1;
1,0,1;
1,0,0,1;
1,1,0,0,1;
MAPLE
g:=sum(t^j*x^j*product(1+x^i, i=j+1..50), j=1..50): gser:=simplify(series(g, x=0, 18)): for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: seq(seq(coeff(P[n], t^j), j=1..n), n=1..14); # Emeric Deutsch, Feb 24 2006
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved