A211388 Expansion of 1/((1-2*x)^6*(1-x)).

1, 13, 97, 545, 2561, 10625, 40193, 141569, 471041, 1496065, 4571137, 13516801, 38862849, 109051905, 299565057, 807600129, 2141192193, 5592842241, 14413725697, 36698062849, 92408905729, 230359564289, 568965726209, 1393398120449

Offset

0,2

Links

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

M. H. Albert, M. D. Atkinson, R. Brignall, The enumeration of three pattern classes using monotone grid classes, El. J. Combinat. 19 (3) (2012) P20. Section 5.5.1

Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.

Index entries for linear recurrences with constant coefficients, signature (13,-72,220,-400,432,-256,64).

Formula

a(n) = 1 + 2^(n-2)*n*(n^4 + 10*n^3 + 55*n^2 + 110*n + 184)/15. - Bruno Berselli, Feb 08 2013

A211386(n) = a(n) - 2*a(n-1). - R. J. Mathar, Feb 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - 2 x)^6 (1 - x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 10 2013 *)
LinearRecurrence[{13, -72, 220, -400, 432, -256, 64}, {1, 13, 97, 545, 2561, 10625, 40193}, 30] (* Harvey P. Dale, Sep 01 2023 *)

Prog

(Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)^6*(1-x)))); // Bruno Berselli, Feb 08 2013

Crossrefs

Cf. A054849 (first differences).

Sequence in context: A141894 A275879 A160554 * A125350 A049294 A198480

Adjacent sequences: A211385 A211386 A211387 * A211389 A211390 A211391

Keyword

nonn,easy

Author

R. J. Mathar, Feb 07 2013

Status

approved