A086950 Binomial transform of decagonal numbers A001107.

0, 1, 12, 60, 224, 720, 2112, 5824, 15360, 39168, 97280, 236544, 565248, 1331200, 3096576, 7127040, 16252928, 36765696, 82575360, 184287232, 408944640, 902823936, 1983905792, 4341104640, 9462349824, 20552089600, 44493176832, 96032784384, 206695301120, 443723808768

Offset: 0

Author

Paul Barry, Jul 24 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Crossrefs

Binomial transform is A086951.

Programs

Magma

[n*2^n*(2*n-1)/2: n in [0..30] ]; // Vincenzo Librandi, Aug 22 2011

Mathematica

LinearRecurrence[{6,-12,8},{0,1,12},30] (* Harvey P. Dale, Dec 13 2015 *)

Formula

a(n) = n*2^n*(2*n-1)/2.

G.f.: x*(1+6*x)/(1-2*x)^3.

a(0)=0, a(1)=1, a(2)=12, a(n)=6*a(n-1)-12*a(n-2)+8*a(n-3). - Harvey P. Dale, Dec 13 2015

E.g.f.: exp(2*x)*x*(1 + 4*x). - Stefano Spezia, Oct 09 2022