A021024 Expansion of 1/((1-x)(1-2x)(1-3x)(1-5x)).

1, 11, 80, 490, 2751, 14721, 76630, 392480, 1990901, 10041031, 50466780, 253122870, 1267989451, 6347088941, 31756902530, 158848951660, 794438206401, 3972771638451, 19865600535880, 99333230758850, 496681840129751, 2483456263849561, 12417422517238830

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-41,61,-30).

Formula

a(n) = stirling2(n+4,4) + stirling2(n+4,5). - Zerinvary Lajos, Oct 04 2007

a(0)=1, a(1)=11, a(2)=80, a(3)=490; for n>3, a(n) = 11*a(n-1) -41*a(n-2) +61*a(n-3) -30*a(n-4). - Vincenzo Librandi, Jul 05 2013

a(n) = 8*a(n-1) -15*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 05 2013

a(n) = (5^(n+3) - 6*3^(n+3) + 8*2^(n+3) - 3)/24. [Yahia Kahloune, Jul 07 2013]

Maple

with(combinat): seq(stirling2(n+4, 4) +stirling2(n+4, 5), n=0..23); # Zerinvary Lajos, Oct 04 2007

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 -5 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-5*x)))); /* or */ I:=[1, 11, 80, 490]; [n le 4 select I[n] else 11*Self(n-1)-41*Self(n-2)+61*Self(n-3)-30*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A159663 A227244 A026897 * A127021 A326243 A091098

Adjacent sequences: A021021 A021022 A021023 * A021025 A021026 A021027

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved