A021814 Expansion of 1/((1-x)(1-4x)(1-6x)(1-8x)).

1, 19, 239, 2519, 24135, 218343, 1903783, 16194343, 135426599, 1118993447, 9166829607, 74629521447, 604827848743, 4885462331431, 39365093814311, 316610553147431, 2543028967600167, 20405121901817895

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,-122,296,-192).

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x)).

a(n) = -1/105 +2^(2n+3)/3 -2^(n+1)*3^(n+3)/5 +8^(n+2)/7. [Bruno Berselli, May 08 2013]

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Bruno Berselli, May 08 2013 *)

Prog

(PARI) Vec(1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x))+O(x^20)) \\ Bruno Berselli, May 08 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x)))); // Bruno Berselli, May 08 2013

Crossrefs

Cf. A019333 (first differences).

Sequence in context: A229026 A114757 A142615 * A299864 A025933 A107203

Adjacent sequences: A021811 A021812 A021813 * A021815 A021816 A021817

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved