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A021124
Expansion of 1/((1-x)(1-2x)(1-5x)(1-7x)).
1
1, 15, 152, 1314, 10479, 79821, 591214, 4301088, 30921077, 220515867, 1563954756, 11049405822, 77854461595, 547524351753, 3845386097978, 26981280929916, 189186857860833, 1325897462045079, 9289229519936080
OFFSET
0,2
FORMULA
a(0)=1, a(1)=15, a(2)=152, a(3)=1314; for n>3, a(n) = 15*a(n-1) -73*a(n-2) +129*a(n-3) -70*a(n-4). - Vincenzo Librandi, Jul 07 2013
a(0)=1, a(1)=15; for n>1, a(n) = 12*a(n-1) -35*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013
a(n) = (2*7^(n+3) - 5^(n+4) + 2^(n+6) - 5)/120. - Yahia Kahloune, Jul 07 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 - 7 x)), {x, 0, 50}], x] (* Harvey P. Dale, Mar 01 2011 *)
LinearRecurrence[{15, -73, 129, -70}, {1, 15, 152, 1314}, 20] (* Vincenzo Librandi, Jul 07 2013 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-7*x)))); /* or */ I:=[1, 15, 152, 1314]; [n le 4 select I[n] else 15*Self(n-1)-73*Self(n-2)+129*Self(n-3)-70*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013
CROSSREFS
Sequence in context: A016103 A206361 A041424 * A004322 A125403 A010035
KEYWORD
nonn,easy
STATUS
approved