A080250 Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).

1, 35, 871, 19215, 402591, 8236095, 166570111, 3349906175, 67183250431, 1345516627455, 26928850135551, 538762184167935, 10777095520297471, 215560428864815615, 4311393762242888191, 86229727095755178495

Offset: 0

Author

Paul Barry, Feb 17 2003

Keywords

• easy
• nonn

Comments

Column k=3 in number triangle A080249.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (35,-354,1120,-800).

Crossrefs

Cf. A080249, A016225, A000292.

Programs

Magma

[(1350*20^n-950*10^n+114*4^n-1)/513: n in [0..20]]; // Vincenzo Librandi, Aug 05 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-4x)(1-10x)(1-20x)),{x,0,20}],x] (* or *) Table[(1350*20^n-950*10^n+114*4^n-1)/513,{n,0,20}] (* or *) LinearRecurrence[{35,-354,1120,-800},{1,35,871,19215},21] (* Harvey P. Dale, Apr 25 2011 *)

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)).

a(n) = (1350*20^n-950*10^n+114*4^n-1)/513.

a(0)=1, a(1)=35, a(2)=871, a(3)=19215, a(n) = 35*a(n-1) -354*a(n-2) +1120*a(n-3) -800*a(n-4). - Harvey P. Dale, Apr 25 2011

Extensions

Corrected by T. D. Noe, Nov 08 2006