OFFSET
0,2
FORMULA
G.f.: -1/(x^2*y^2 - (1 - x*(y + 2*A001263(x, y) + 1))^2) = 1/(1 - 2*x^2*y + x^2 - 2*x*y - 2*x).
EXAMPLE
1,
2, 2,
3, 10, 4,
4, 28, 32, 8,
5, 60, 136, 88, 16
MAPLE
ogf := 1/(1 -2*x^2*y + x^2 - 2*x*y - 2*x): ser := series(ogf, x, 22):
xser := n -> expand(coeff(ser, x, n)):
seq(seq(coeff(xser(n), y, k), k=0..n), n=0..10); # Peter Luschny, Oct 23 2020
PROG
(Maxima)
T(n, m):=sum((binomial(m-k+2, k-1)*binomial(n+1, k-1)*binomial(n-m+k-1, k-1)*binomial(2*n-2*k+4, 2*m-4*k+5))/(binomial(2*k-2, k-1)*binomial(2*m-2*k+4, 2*k-2)), k, 1, (m+3)/2)/2;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Oct 23 2020
STATUS
approved