OFFSET
0,2
FORMULA
G.f.: (1/(1-x-x*y-4*x^2*y/(1-x-x*y)))^2.
T(n,m) = Sum_{k=0..n} C(n+1,2*k+1)*C(n-2*k,m-k)*(k+1)*4^k.
A045563(n) = (Sum_{m=0..n} T(n,m))/2^n.
EXAMPLE
1,
2, 2,
3, 14, 3,
4, 44, 44, 4,
5, 100, 238, 100, 5,
6, 190, 828, 828, 190, 6,
7, 322, 2233, 4092, 2233, 322, 7
MATHEMATICA
Table[Sum[Binomial[n + 1, 2 k + 1] Binomial[n - 2 k, m - k] (k + 1)*4^k, {k, 0, n} ], {n, 0, 9}, {m, 0, n}] // Flatten (* Michael De Vlieger, Nov 04 2020 *)
PROG
(Maxima)
T(n, m):=((2*m*n+2*n-2*m^2+1)*binomial(2*n+2, 2*m+1))/(4*n+2);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Nov 01 2020
STATUS
approved