A320327 - OEIS

%I #11 Oct 14 2018 11:57:51

%S 1,1,2,1,3,12,18,12,3,10,60,150,200,150,60,10,35,280,980,1960,2450,

%T 1960,980,280,35,126,1260,5670,15120,26460,31752,26460,15120,5670,

%U 1260,126,462,5544,30492,101640,228690,365904,426888,365904,228690,101640,30492,5544,462

%N Triangle T(n,m) = C(2*n,m)*C(2*n-1,n), 0 <= m <= 2*n, n >= 0.

%F G.f.: (2*x*y^2 + 4*x*y + 2*x)/(sqrt(-4*x*y^2 - 8*x*y - 4*x + 1) + 4*x*y^2 + 8*x*y + 4*x - 1).

%e Triangle begins

%e     1;

%e     1,    2,    1;

%e     3,   12,   18,    12,     3;

%e    10,   60,  150,   200,   150,    60,    10;

%e    35,  280,  980,  1960,  2450,  1960,   980,   280,   35;

%e   126, 1260, 5670, 15120, 26460, 31752, 26460, 15120, 5670, 1260, 126;

%p a:=(n,m)->binomial(2*n,m)*binomial(2*n-1,n): seq(seq(a(n,m),m=0..2*n),n=0..6); # _Muniru A Asiru_, Oct 12 2018

%o (GAP) Flat(List([0..6],n->List([0..2*n],m->Binomial(2*n,m)*Binomial(2*n-1,n)))); # _Muniru A Asiru_, Oct 12 2018

%K nonn,tabf

%O 0,3

%A _Vladimir Kruchinin_, Oct 10 2018