A027319 a(n) = Sum_{k=0..m} (k+1) * A026082(n, k), where 0 <= k <= m, m=n for n=0,1,2,3; m=2n for n >= 4.

1, 3, 8, 20, 120, 432, 1512, 5184, 17496, 58320, 192456, 629856, 2047032, 6613488, 21257640, 68024448, 216827928, 688747536, 2181033864, 6887475360, 21695547384, 68186006064, 213856109928, 669462604992, 2092070640600, 6527260398672, 20334926626632

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Or, a(n) = Sum_{k=0..m} (k+1)*T(n,m-k), m=n for n=0,1,2,3; m=2n for n >= 4; T given by A026082.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-9).

Programs

Mathematica

CoefficientList[Series[(1 - 3 x - x^2 - x^3 + 72 x^4 - 108 x^5)/(1 - 3 x)^2, {x, 0, 26}], x] (* Michael De Vlieger, Feb 17 2016 *)

PARI

Vec((1-3*x-x^2-x^3+72*x^4-108*x^5)/(1-3*x)^2 + O(x^30)) \\ Colin Barker, Feb 17 2016

Formula

For n>3, a(n) = 8*(n+1)*3^(n-3).

From Colin Barker, Feb 17 2016: (Start)

a(n) = 6*a(n-1) - 9*a(n-2) for n>5.

G.f.: (1 - 3*x - x^2 - x^3 + 72*x^4 - 108*x^5) / (1-3*x)^2.

(End)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007