A027971 T(n, 2n-9), T given by A027960.

3, 7, 18, 47, 123, 319, 806, 1954, 4506, 9859, 20495, 40615, 77040, 140455, 247085, 420906, 696509, 1122751, 1767344, 2722551, 4112177, 6100063, 8900312, 12789498, 18121132, 25342683, 35015477, 47837823, 64671742

Offset: 5

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

A column of triangle A027011.

Programs

GAP

a:=[3,7,18,47, 123,319,806,1954,4506,9859];; for n in [11..40] do a[n]:=10*a[n-1]-45*a[n-2]+120*a[n-3]-210*a[n-4]+252*a[n-5]-210*a[n-6] +120*a[n-7] -45*a[n-8]+10*a[n-9]-a[n-10]; od; a; # G. C. Greubel, Sep 26 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^5*(3 -2*x)*(1-7*x+23*x^2-44*x^3+55*x^4-44*x^5+23*x^6-7*x^7+x^8)/(1-x)^10 )); // G. C. Greubel, Sep 26 2019

Maple

seq(coeff(series(x^5*(3-2*x)*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7 +x^8)/(1-x)^10, x, n+1), x, n), n = 5..40); # G. C. Greubel, Sep 26 2019

Mathematica

LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1}, {3,7,18,47, 123,319,806,1954,4506,9859},40] (* Harvey P. Dale, Aug 04 2017 *)

PARI

Vec(-x^5*(2*x-3)*(x^8-7*x^7+23*x^6-44*x^5+55*x^4-44*x^3+23*x^2 -7*x+1)/(x-1)^10 + O(x^40)) \\ Colin Barker, Nov 25 2014

Sage

def A027971_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x^5*(3-2*x)*(1-7*x+23*x^2-44*x^3+55*x^4-44*x^5+23*x^6-7*x^7 +x^8)/(1-x)^10 ).list()
a=A027971_list(40); a[5:] # G. C. Greubel, Sep 26 2019

Formula

a(n) = (17055360 -16329024*n +7697736*n^2 -2299060*n^3 +462798*n^4 -60207*n^5 +4284*n^6 -30*n^7 -18*n^8 +n^9)/362880. - Colin Barker, Nov 25 2014

G.f.: x^5*(3-2*x)*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7 +x^8)/(1-x)^10. - Colin Barker, Nov 25 2014