login
A320327
Triangle T(n,m) = C(2*n,m)*C(2*n-1,n), 0 <= m <= 2*n, n >= 0.
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
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
KEYWORD
nonn,tabf
AUTHOR
Vladimir Kruchinin, Oct 10 2018
STATUS
approved