OFFSET
2,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1276
R. C. Read, Contributions to the cell growth problem, Canad. J. Math., 14 (1962), 1-20.
FORMULA
T(n, k) = Sum_v C(n-k+1, 2*k-n-v)*C(n-k+v, n-k).
G.f. (1+x*y)^2/(1-x*y)*1/((1-x*y)-(1+x*y)*x^2*y). - Christopher Hanusa (chanusa(AT)math.washington.edu), Sep 22 2004
T(n,k) = 0 for n > 2*k. - Andrew Howroyd, Oct 02 2017
EXAMPLE
Triangle begins:
1;
0, 4;
0, 1, 8;
0, 0, 6, 12;
0, 0, 1, 18, 16;
0, 0, 0, 8, 38, 20;
0, 0, 0, 1, 32, 66, 24;
...
MAPLE
with(combinat): for n from 2 to 30 do for k from 1 to n-1 do printf(`%d, `, sum(binomial(n-k+1, 2*k-n-v)*binomial(n-k+v, n-k), v=0..k) ) od:od:
MATHEMATICA
t[n_, k_] := Sum[Binomial[n-k+1, 2*k-n-v]*Binomial[n-k+v, n-k], {v, 0, k}]; Table[t[n, k], {n, 2, 15}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Dec 20 2013 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Feb 05 2001
EXTENSIONS
More terms from James A. Sellers, Feb 06 2001
STATUS
approved