A020447 Expansion of 1/((1-5*x) * (1-8*x) * (1-11*x)).

1, 24, 393, 5480, 70161, 853944, 10066393, 116192520, 1322205921, 14898923864, 166735197993, 1856912289960, 20608880226481, 228161663489784, 2521496249891193, 27830232878409800, 306882907287251841, 3381715508097175704, 37246902627265441993, 410100204278978264040

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-183,440).

Formula

a(n) = 25*5^n/18 -64*8^n/9 +121*11^n/18. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=24, a(2)=393; for n>2, a(n) = 24*a(n-1) -183*a(n-2) +440*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 19*a(n-1) -88*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

From Seiichi Manyama, May 05 2025: (Start)

a(n) = Sum_{k=0..n} 3^k * 5^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).

a(n) = Sum_{k=0..n} (-3)^k * 11^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{24, -183, 440}, {1, 24, 393}, 30] (* Harvey P. Dale, Jun 20 2015 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-11*x)))); // Vincenzo Librandi, Jul 03 2013
(Magma) I:=[1, 24, 393]; [n le 3 select I[n] else 24*Self(n-1)-183*Self(n-2)+440*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Cf. A016223, A016297, A017933, A019618.

Sequence in context: A025947 A007752 A145602 * A021894 A021694 A395787

Adjacent sequences: A020444 A020445 A020446 * A020448 A020449 A020450

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved