A084900 a(n) = 3^(n-2)*n*(5*n+1)/2.

0, 1, 11, 72, 378, 1755, 7533, 30618, 119556, 452709, 1673055, 6062364, 21611934, 75996063, 264126177, 908764110, 3099363912, 10489051017, 35255264499, 117775828656, 391294693890, 1293597012771, 4257363753621, 13954111172802

Offset: 0

Author

Paul Barry, Jun 10 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A084899. Second binomial transform of heptagonal numbers A000566. Third binomial transform of (0,1,5,0,0,0,...).

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Crossrefs

Cf. A000566, A084899, A084901.

Programs

Mathematica

Table[(3^(n-2) n(5n+1))/2,{n,0,30}] (* or *) LinearRecurrence[{9,-27,27},{0,1,11},30] (* Harvey P. Dale, Jul 21 2016 *)

Formula

G.f.: x*(1 + 2*x)/(1 - 3*x)^3.

E.g.f.: exp(3*x)*x*(2 + 5*x)/2. - Stefano Spezia, Oct 28 2023