A123890 Expansion of g.f.: x/((1-x^2)^5 - 1 + x).

1, 5, 25, 115, 525, 2385, 10825, 49120, 222875, 1011251, 4588335, 20818575, 94459755, 428590575, 1944636420, 8823364350, 40034094615, 181645987625, 824179118751, 3739533301365, 16967318139775, 76985511735170, 349304997307275, 1584895370489480

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. Burstein and T. Mansour, Words restricted by 3-letter ..., arXiv:math/0112281 [math.CO], 2001.

A. Burstein and T. Mansour, Words Restricted by 3-Letter Generalized Multipermutation Patterns, Annals. Combin., 7 (2003), 1-14.

Index entries for linear recurrences with constant coefficients, signature (5,0,-10,0,10,0,-5,0,1).

Maple

seq(coeff(series(1/(1-5*x+10*x^3-10*x^5+5*x^7-x^9), x, n+1), x, n), n = 0 .. 30); # G. C. Greubel, Aug 07 2019

Mathematica

CoefficientList[Series[x/((1-x^2)^5 -1+x), {x, 0, 30}], x] (* G. C. Greubel, Aug 07 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(x/((1-x^2)^5 -1+x)) \\ G. C. Greubel, Aug 07 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x/((1-x^2)^5 -1+x) )); // G. C. Greubel, Aug 07 2019
(Sage)
def A123890_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x/((1-x^2)^5 -1+x) ).list()
A123890_list(30) # G. C. Greubel, Aug 07 2019
(GAP) a:=[1, 5, 25, 115, 525, 2385, 10825, 49120, 222875];; for n in [10..30] do a[n]:=5*a[n-1]-10*a[n-3] +10*a[n-5]-5*a[n-7]+a[n-9]; od; a; # G. C. Greubel, Aug 07 2019

Crossrefs

Sequence in context: A261383 A089947 A267467 * A123894 A200781 A055297

Adjacent sequences: A123887 A123888 A123889 * A123891 A123892 A123893

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2006

Status

approved