A021202 Expansion of 1/((1-x)(1-2x)(1-6x)(1-10x)).

1, 19, 251, 2891, 31227, 326235, 3346267, 33966427, 342687323, 3445012571, 34558963803, 346242670683, 3466344910939, 34686958350427, 347010638983259, 3470952722772059, 34714605225488475, 347176520241754203, 3471948010339283035, 34720576950924324955

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (19,-110,212,-120).

Formula

a(n) = ( 5*10^(n+3)-18*6^(n+3)+45*2^(n+3)-32 )/1440. - Yahia Kahloune, May 20 2013

a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -60*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=19, a(2)=251, a(3)=2891; for n>3, a(n) = 19*a(n-1) -110*a(n-2) +212*a(n-3) -120*a(n-4). - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{19, -110, 212, -120}, {1, 19, 251, 2891}, 30] (* Harvey P. Dale, Apr 26 2015 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 19, 251, 2891]; [n le 4 select I[n] else 19*Self(n-1)-110*Self(n-2)+212*Self(n-3)-120*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A021464 A017998 A018912 * A125454 A293917 A009762

Adjacent sequences: A021199 A021200 A021201 * A021203 A021204 A021205

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved