OFFSET
0,2
COMMENTS
LINKS
Wolfdieter Lang, First rows of the triangle.
FORMULA
a(n,m) = denominator(R(n,m)) with the rationals Riordan matrix elements R(n,m)= [x^m]R(n,x), with the row polynomials R(n,x) generated by ((2 - c(z/4))/(1-z))/(1 - x*(-1 + c(z/4))) = 2*((1+x)*(z-1) + (1-x)*sqrt(1-z))/((1-z)*((1+x)^2*z - 4*x)), where c(x) is the o.g.f. of the Catalan numbers A000108.
EXAMPLE
The triangle a(n,m) begins:
n\m 0 1 2 3 4 5 6 ...
0: 1
1: 4 4
2: 8 16 16
3: 64 64 64 64
4: 128 64 64 256 256
5: 512 512 1024 1024 1024 1024
6: 1024 4096 4096 2048 2048 4096 4096
...
For more rows see the link.
For the rational triangle R(n,m) see the example section of A244420.
Expansion: x^3 = (35*Todd(0, x) + 21*Todd(1, x) + 7*Todd(2, x) + 1*Todd(3, x))/64 = (35 + 21*(-3+4*x) + 7*( 5-20*x+16*x^2) + (-7+56*x-112*x^2+64*x^3))/64. For the Todd polynomials see A084930.
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Aug 04 2014
STATUS
approved