OFFSET
0,3
LINKS
T. Coates, A. Corti, S. Galkin, V. Golyshev, and A. Kasprzy, Mirror Symmetry and Fano Manifolds, arXiv:1212.1722 [math.AG], 2012. Example 3.6.
FORMULA
a(n) = Sum_{j=ceiling(n/3)..floor(n/2)} C(n-j,n-2j)*C(j,n-2j)*C(n,j). - Devin Akman and Ricardo Acuna, Dec 18 2023
EXAMPLE
For n=3, (x + x*y + y +1/(x*y))^3 = x^3 y^3 + 1/(x^3*y^3) + 3 x^3 y^2 + 3 x^3 y + x^3 + 3 x^2 y^3 + 6 x^2 y^2 + 3 x^2 y + 3/(x^2*y) + 3 x y^3 + 3 x y^2 + 3/(x*y^2) + 3 x y + (3 x)/y + (3 y)/x + 3/(x*y) + 6 x + y^3 + 6 y + 6, so a(3) = 6.
PROG
(Sage)
def a(n):
return sum([binomial(n-j, n-2*j)*binomial(j, n-2*j)*binomial(n, j)
for j in [ceil(n/3)..floor(n/2)]])
(PARI) a(n) = sum(j=ceil(n/3), floor(n/2), binomial(n-j, n-2*j)*binomial(j, n-2*j)*binomial(n, j)); \\ Michel Marcus, Dec 22 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ricardo Acuna, Sep 30 2022
STATUS
approved