OFFSET
0,4
FORMULA
G.f.: sin(arcsin(216*x^2*(y+1)^2-1)/3)/6+13/12.
G.f.: 1+x*(sqrt(3)/2)*(sech(arccosh(-sqrt(108)*x*(1+y))/3))*(1+y).
EXAMPLE
Triangle T(n, m) starts:
[0] 1;
[1] 1, 1;
[2] 2, 4, 2;
[3] 10, 30, 30, 10;
[4] 64, 256, 384, 256, 64;
[5] 462, 2310, 4620, 4620, 2310, 462;
[6] 3584, 21504, 53760, 71680, 53760, 21504, 3584;
[7] 29172, 204204, 612612, 1021020,1021020, 612612, 204204, 29172;
MATHEMATICA
T[0, 0] = 1;
T[n_, m_] := 4^(n-1)*Binomial[n, m]*Binomial[3n/2-2, n-1]/n;
Table[T[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Feb 16 2023 *)
PROG
(Maxima)
T(n, m):=if n=0 and m=0 then 1 else if n=0 then 0 else (4^(n-1)*binomial(n, m)*binomial((3*n)/2-2, n-1))/(n);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 16 2023
STATUS
approved