OFFSET
0,6
COMMENTS
FORMULA
G.f.: A(x, y)=(1-2*x*y+2*x^2*y^2)/((1-x*y)*(1-x*y-x^2*y^2-x*(1-x*y))).
EXAMPLE
Rows begin:
[1],
[1,0],
[1,0,2],
[1,0,3,3],
[1,0,4,4,6],
[1,0,5,5,10,10],
[1,0,6,6,15,18,17],
[1,0,7,7,21,28,35,28],
[1,0,8,8,28,40,60,64,46],...
where row sums form 2^n-1 for n>0:
2^1-1 = 1+0 = 1
2^2-1 = 1+0+2 = 3
2^3-1 = 1+0+3+3 = 7
2^4-1 = 1+0+4+4+6 = 15
2^5-1 = 1+0+5+5+10+10 = 31.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0, 1, polcoeff(((1+x+sqrt(1-2*x+5*x^2+x*O(x^k)))/2)^n, k)))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 28 2004
STATUS
approved