A028322 Central elements in the 5-Pascal triangle A028313.

1, 5, 12, 38, 130, 462, 1680, 6204, 23166, 87230, 330616, 1259700, 4820452, 18513068, 71318400, 275467320, 1066432950, 4136847390, 16075953960, 62570669700, 243882320220, 951797460900, 3718872587040, 14545727618760

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A000984, A028313.

Programs

Magma

[(n+1)*(7*n-2)*Catalan(n)/(2*(2*n-1)): n in [0..40]]; // G. C. Greubel, Jan 05 2024

Mathematica

Table[(n+1)*(7*n-2)*CatalanNumber[n]/(2*(2*n-1)), {n,0,40}] (* G. C. Greubel, Jan 05 2024 *)

SageMath

[(7*n-2)*binomial(2*n,n)/(2*(2*n-1)) for n in range(41)] # G. C. Greubel, Jan 05 2024

Formula

G.f.: (1 + 3*x)/sqrt(1-4*x). - Vladeta Jovovic, Jan 08 2004

a(n) = A000984(n) + 3*A000984(n-1). - R. J. Mathar, Dec 15 2015

a(n) = (n+1)*(7*n-2)*A000108(n)/(2*(2*n-1)). - G. C. Greubel, Jan 05 2024

Extensions

More terms from James Sellers