A120663 Expansion of x*(67 +2476*x +38216*x^2 -124633*x^3 +129444*x^4)/((1-x)*(1+x)*(1-2*x)*(1+3*x)*(1-4*x)*(1-6*x)).

0, 67, 3079, 65458, 436705, 3325420, 21257887, 137628082, 852017725, 5260500568, 32028617995, 194422680046, 1174383558985, 7081178928436, 42616157629303, 256244634375850, 1539564650731285, 9246057306575824, 55510175964258211

Offset

0,2

Links

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

Roger L. Bagula, Mathematica program for A120663

Index entries for linear recurrences with constant coefficients, signature (9,-7,-93,152,84,-144).

Formula

G.f.: x*(67 +2476*x +38216*x^2 -124633*x^3 +129444*x^4)/((1-x)*(1+x)*(1-2*x)*(1+3*x)*(1-4*x)*(1-6*x)). - Colin Barker, Nov 01 2012

Mathematica

See link for Mathematica program that uses matrices.
LinearRecurrence[{9, -7, -93, 152, 84, -144}, {0, 67, 3079, 65458, 436705, 3325420}, 31] (* G. C. Greubel, Dec 26 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(67+2476*x+38216*x^2-124633*x^3+129444*x^4)/(1-9*x+7*x^2+93*x^3 - 152*x^4-84*x^5+144*x^6) )); // G. C. Greubel, Dec 26 2022
(SageMath)
def f(x): return x*(67+2476*x+38216*x^2-124633*x^3+129444*x^4)/(1-9*x+7*x^2+93*x^3-152*x^4-84*x^5+144*x^6)
def A120663_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(x) ).list()
A120663_list(30) # G. C. Greubel, Dec 26 2022

Crossrefs

Sequence in context: A226713 A069397 A103727 * A261974 A328353 A078989

Adjacent sequences: A120660 A120661 A120662 * A120664 A120665 A120666

Keyword

nonn,easy,less

Author

Roger L. Bagula, Aug 10 2006

Extensions

Edited by N. J. A. Sloane, Jul 13 2007

Meaningful name using g.f. from Joerg Arndt, Dec 26 2022

Status

approved