OFFSET
0,4
COMMENTS
T(n,k) is the number of paths in the first quadrant, starting from the origin, with unit steps up, down, right, or left, having a total of n steps, exactly k of which are vertical (up or down). Example: T(3,2)=6 because we have NNE, NEN, ENN, NSE, ENS and NES. [Emeric Deutsch, Nov 22 2008]
LINKS
David M. Bloom et al., A Convolution of Middle Binomial Coefficients: Problem 10921, Amer. Math. Monthly 110, (2003), 958-959.
E. Deutsch and D. Lovit, Problem 1739, Math. Magazine, vol. 80, No. 1, 2007, p. 80. [Emeric Deutsch, Nov 22 2008]
FORMULA
T(n, k) = binomial(n, k)*binomial(k, floor(k/2))*binomial(n-k, floor((n-k)/2)) (0<=k<=n).
MAPLE
T:=(n, k)->binomial(n, k)*binomial(k, floor(k/2))*binomial(n-k, floor((n-k)/2)): for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Apr 23 2005
STATUS
approved