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A016091
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Expansion of 1/((1-8x)(1-9x)(1-10x)(1-12x)).
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1
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1, 39, 955, 18795, 325171, 5167659, 77353795, 1107933915, 15345293491, 207057429579, 2736619356835, 35572444360635, 456191563128211, 5785999811488299, 72719715037363075, 907085298655532955
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 39*a(n-1) - 566*a(n-2) + 3624*a(n-3) - 8640*a(n-4) for n >= 4.
a(n) = 22*a(n-1) - 120*a(n-2) + 9^(n+1) - 8^(n+1) for n >= 2. (End)
a(n) = -8^(n+2) + 3*9^(n+2) - 25*10^(n+1) + 6*12^(n+1). - R. J. Mathar, Mar 18 2011
E.g.f.: exp(8*x)*(72*exp(4*x) - 250*exp(2*x) + 243*exp(x) - 64). - Stefano Spezia, Aug 14 2022
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)
LinearRecurrence[{39, -566, 3624, -8640}, {1, 39, 955, 18795}, 30] (* Harvey P. Dale, Jul 08 2019 *)
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PROG
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(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-10*x)*(1-12*x)))); /* or */ I:=[1, 39, 955, 18795]; [n le 4 select I[n] else 39*Self(n-1)-566*Self(n-2)+3624*Self(n-3)-8640*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Jun 24 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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