OFFSET
1,2
FORMULA
G.f.: 1/(1-(1-sqrt(x*(-4*x^5-16*x^4-24*x^3-16*x^2-4*x)*y+1))/(2*x^3+4*x^2+2*x)).
EXAMPLE
1,
2,1,
1,5,1,
0,12,8,1,
0,19,33,11,1,
0,21,96,63,14,1,
0,15,217,256,102,17,1
MATHEMATICA
T[n_, m_] := Sum[k * Binomial[2*m - k - 1, m - k] * Binomial[2*(2*m - k), n - 2*m + k], {k, 1, m}] / m; Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* Amiram Eldar, Oct 08 2020 *)
PROG
(Maxima)
T(n, m):=sum(k*binomial(2*m-k-1, m-k)*binomial(2*(2*m-k), n-2*m+k), k, 1, m)/m;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Oct 07 2020
STATUS
approved