A021784 Expansion of 1/((1-x)(1-4x)(1-5x)(1-11x)).

1, 21, 302, 3762, 43923, 497223, 5545264, 61398804, 677478725, 7463074905, 82149266706, 903924739926, 9944608539607, 109397965416267, 1203414334895828, 13237742692094328, 145616100380861769

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,-139,339,-220).

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x)).

a(n) = -1/120 +2^(2n+6)/21 -5^(n+3)/24 +11^(n+3)/420. - Bruno Berselli, May 08 2013

a(n) = 21*a(n-1) - 139*a(n-2) + 339*a(n-3) - 220*a(n-4). - Wesley Ivan Hurt, Jan 01 2024

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 5 x) (1 - 11 x)), {x, 0, 20}], x] (* Bruno Berselli, May 08 2013 *)
LinearRecurrence[{21, -139, 339, -220}, {1, 21, 302, 3762}, 20] (* Harvey P. Dale, Feb 07 2025 *)

Prog

(PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x))+O(x^20)) \\ Bruno Berselli, May 08 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-11*x)))); // Bruno Berselli, May 08 2013

Crossrefs

Cf. A019040 (first differences).

Sequence in context: A019839 A077513 A079517 * A019618 A081553 A021524

Adjacent sequences: A021781 A021782 A021783 * A021785 A021786 A021787

Keyword

nonn,easy,changed

Author

N. J. A. Sloane.

Status

approved