g:= 1+sum((-1)^n*z^(2*n+1)*(1-z)/(product((1-z)*(1-z^i)-z, i=1..n+1)), n=0..40): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..30); #
Emeric Deutsch, Mar 05 2008
# Alternative:
b:= proc(x, y, k, t) option remember; `if`(x=0, 1, `if`(y>0,
`if`(t=1 and y>k, 0, b(x-1, y-1, `if`(t=1, min(k, y),
k), 0)), 0) +`if`(y<x-1, b(x-1, y+1, k, 1), 0))
end:
a:= n-> b(2*n, 0, n, 0):
# Alternative:
b:= proc(n, i) option remember; `if`(n=0, 1, add(
binomial(i, j)*add(b(n-2-(i-j)*2-2*t, i-j+t),
t=0..n/2+j-i-1), j=0..i))
end:
a:= n-> b(2*n, 0):
