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

Author

R. J. Mathar, Feb 07 2013

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A054849 (first differences).

Programs

Magma

m:=24; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)^6*(1-x)))); // Bruno Berselli, 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 *)

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