A081915 a(n) = 4^n*(n^3 - 3n^2 + 2n + 384)/384.

1, 4, 16, 65, 272, 1184, 5376, 25344, 122880, 606208, 3014656, 15007744, 74448896, 367001600, 1795162112, 8707375104, 41875931136, 199715979264, 944892805120, 4436701216768, 20684562497536, 95794950569984, 440904162738176

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081914. 4th binomial transform of (1,0,0,1,0,0,0,0,...). Case k=4 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f.: (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..150
• Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256)

Crossrefs

Cf. A081916.

Programs

Magma

[4^n*(n^3-3*n^2+2*n+384)/384: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Mathematica

LinearRecurrence[{16,-96,256,-256},{1,4,16,65},30] (* Harvey P. Dale, Aug 14 2017 *)
CoefficientList[Series[(1 - 12x + 48x^2 - 63x^3)/(1-4x)^4 ,{x, 0, 30}], x] (* Stefano Spezia, Sep 02 2018 *)

PARI

a(n)=4^n*(n^3-3*n^2+2*n+384)/384 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 4^n*(n^3 - 3n^2 + 2n + 384)/384.

G.f.: (1 - 12x + 48x^2 - 63x^3)/(1-4x)^4.