OFFSET
1,1
COMMENTS
FORMULA
T(n,2k) = 2*binomial(n-1,k-1)*binomial(n-1,k);
T(n,2k-1) = 2*binomial(n-1,k-1)^2.
G.f.: [1+t*r(t^2,z)]/[1-t*r(t^2,z)], where r(t,z) is the Narayana function, defined by r = z(1+r)(1+tr).
EXAMPLE
T(3,2)=4 because we have ENNNEE, EENNNE, NEEENN and NNEEEN.
Triangle starts:
2;
2,2,2;
2,4,8,4,2;
2,6,18,18,18,6,2;
2,8,32,48,72,48,32,8,2;
MAPLE
T := proc (n, k) if `mod`(k, 2) = 0 then 2*binomial(n-1, (1/2)*k-1)*binomial(n-1, (1/2)*k) else 2*binomial(n-1, (1/2)*k-1/2)^2 end if end proc: for n to 9 do seq(T(n, k), k = 1 .. 2*n-1) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 10 2008
STATUS
approved