A021524 Expansion of 1/((1-x)*(1-3*x)*(1-6*x)*(1-11*x)).

1, 21, 304, 3822, 45031, 513639, 5760910, 64038576, 708445573, 7817058249, 86132670988, 948329828082, 10436851589347, 114836710756971, 1263391885146058, 13898439159046260, 152889601348716673, 1681826238624840525, 18500332368188119240, 203505118511701944630, 2238565078403747365471

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-137,315,-198).

Formula

a(n) = (3*11^(n+3) - 16*6^(n+3) + 25*3^(n+3) - 12)/1200. - Yahia Kahloune, Jun 30 2013

From Vincenzo Librandi, Jul 10 2013: (Start)

a(0)=1, a(1)=21; for n>1, a(n) = 17*a(n-1) - 66*a(n-2) + (3^(n+1) - 1)/2.

a(0)=1, a(1)=21, a(2)=304, a(3)=3822; for n>3, a(n) = 21*a(n-1) - 137*a(n-2) + 315*a(n-3) - 198*a(n-4). (End)

E.g.f.: exp(x)*(-4 + 225*exp(2*x) - 1152*exp(5*x) + 1331*exp(10*x))/400. - Stefano Spezia, Jun 03 2026

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-11*x)))); // Vincenzo Librandi, Jul 10 2013
(Magma) I:=[1, 21, 304, 3822]; [n le 4 select I[n] else 21*Self(n-1)-137*Self(n-2)+315*Self(n-3)-198*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A021784 A019618 A081553 * A021268 A018069 A019488

Adjacent sequences: A021521 A021522 A021523 * A021525 A021526 A021527

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved