OFFSET
0,4
LINKS
H. Prodinger, The Kernel Method: a collection of examples, Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp.
FORMULA
G.f.: r(z)/(z(1+z)(1-r(z)))*(1+xzr(z))/(1-xr(z)), with r(z)=(1-sqrt(1-4z^2)/2z. Then the g.f. of the k-th column is r(z)^(k+1)/(z(1-r(z))).
T(n, k) = Sum_{i=0..n} (-1)^(n-i)*C(i, floor(i/2)) for k=0, otherwise T(n, k) = C(n, floor((n-k)/2)).
EXAMPLE
1,
0,1,
2,1,1,
1,3,1,1,
5,4,4,1,1,
5,10,5,5,1,1,
15,15,15,6,6,1,1,
20,35,21,21,7,7,1,1,
50,56,56,28,28,8,8,1,1,
76,126,84,84,36,36,9,9,1,1,
PROG
(PARI) T(n, k) = if (k==0, sum(i=0, n, (-1)^(n-i)*binomial(i, i\2)), binomial(n, (n-k)\2));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print(); ); \\ Michel Marcus, Dec 04 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ralf Stephan, Jan 21 2005
STATUS
approved