A021464 Expansion of 1/((1-x)(1-3x)(1-5x)(1-10x)).

1, 19, 248, 2810, 29871, 307929, 3126478, 31504000, 316245941, 3168518639, 31715571108, 317307900390, 3173840747611, 31742218586149, 317441248586138, 3174507821007980, 31745554950382881, 317457933399054459

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,-113,245,-150).

Formula

a(n) = (8*10^(n+3) - 63*5^(n+3) + 90*3^(n+3) - 35)/2520. - Yahia Kahloune, May 19 2013

a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1)-50*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=19, a(2)=248, a(3)=2810; for n>3, a(n) = 19*a(n-1) -113*a(n-2) +245*a(n-3) -150*a(n-4). - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 -10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)
LinearRecurrence[{19, -113, 245, -150}, {1, 19, 248, 2810}, 30] (* Harvey P. Dale, Aug 05 2019 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-10*x)))); /* or */ I:=[1, 19, 248, 2810]; [n le 4 select I[n] else 19*Self(n-1)-113*Self(n-2)+245*Self(n-3)-150*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A318194 A019443 A021229 * A017998 A018912 A021202

Adjacent sequences: A021461 A021462 A021463 * A021465 A021466 A021467

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved