A320327 Triangle T(n,m) = C(2*n,m)*C(2*n-1,n), 0 <= m <= 2*n, n >= 0.

1, 1, 2, 1, 3, 12, 18, 12, 3, 10, 60, 150, 200, 150, 60, 10, 35, 280, 980, 1960, 2450, 1960, 980, 280, 35, 126, 1260, 5670, 15120, 26460, 31752, 26460, 15120, 5670, 1260, 126, 462, 5544, 30492, 101640, 228690, 365904, 426888, 365904, 228690, 101640, 30492, 5544, 462

Offset

0,3

Links

Table of n, a(n) for n=0..48.

Formula

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).

Example

Triangle begins
    1;
    1,    2,    1;
    3,   12,   18,    12,     3;
   10,   60,  150,   200,   150,    60,    10;
   35,  280,  980,  1960,  2450,  1960,   980,   280,   35;
  126, 1260, 5670, 15120, 26460, 31752, 26460, 15120, 5670, 1260, 126;

Maple

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

Prog

(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

Crossrefs

Sequence in context: A168217 A329025 A317548 * A366591 A007447 A153189

Adjacent sequences: A320324 A320325 A320326 * A320328 A320329 A320330

Keyword

nonn,tabf

Author

Vladimir Kruchinin, Oct 10 2018

Status

approved