OFFSET
1,1
COMMENTS
FORMULA
T(n, k)=2^(n-k+1)*binomial(n, k)*binomial(n, k-1)/n (1<=k<=n). G.f. G=G(t, z) satisfies G=z(2+G)(t+G).
EXAMPLE
T(3,3)=2 because we have (U)D(U)D(H) and (U)D(U)D(U)D, where U=(1,1), D=(1,-1) and H=(2,0) (the weak ascents are shown between parentheses).
Triangle starts:
2;
4,2;
8,12,2;
16,48,24,2;
32,160,160,40,2.
MAPLE
T:=(n, k)->2^(n-k+1)*binomial(n, k)*binomial(n, k-1)/n: for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
Flatten[Table[2^(n-k+1) Binomial[n, k] Binomial[n, k-1]/n, {n, 10}, {k, n}]] (* Harvey P. Dale, Oct 01 2011 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Dec 23 2005
EXTENSIONS
Keyword tabf changed to tabl by Michel Marcus, Apr 09 2013
STATUS
approved