A011780 Expansion of 1/((1-2*x)^3*(1-x^2)^2).

1, 6, 26, 92, 291, 850, 2348, 6216, 15925, 39742, 97086, 233012, 550983, 1286442, 2970960, 6796320, 15417945, 34719510, 77672290, 172743180, 382147691, 841346306, 1844250996, 4026531832, 8758949501, 18989322990, 41040798598, 88444511716, 190092071055, 407544674522, 871719288216, 1860516203472

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-10,-4,23,-10,-12,8).

Formula

a(n) = (3*n^2 +n +10)*2^(n+3)/27 +(n/4 +1)*(-1)^n/27 -n/4 -2. - Bruno Berselli, Jun 24 2013

E.g.f.: (1/108)*( (4-x)*exp(-x) - 27*(8+x)*exp(x) + 64*(5+4*x+6*x^2)*exp(2*x) ). - G. C. Greubel, Oct 22 2024

Mathematica

CoefficientList[Series[1/((1-2 x)^3 (1-x^2)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 23 2013 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!(1/(1-2*x)^3/(1-x^2)^2)); // Vincenzo Librandi, Jun 24 2013
(SageMath)
def A011780(n): return (2^(n+5)*(10 +n +3*n^2) +(-1)^n*(4+n) -27*n -216)//108
[A011780(n) for n in range(41)] # G. C. Greubel, Oct 22 2024

Crossrefs

Sequence in context: A166214 A032169 A032196 * A036631 A224288 A036638

Adjacent sequences: A011777 A011778 A011779 * A011781 A011782 A011783

Keyword

nonn,easy

Author

Emeric Deutsch

Status

approved