A027972 T(n, 2n-10), T given by A027960.

1, 4, 11, 29, 76, 199, 518, 1324, 3278, 7784, 17643, 38138, 78753, 155793, 296248, 543333, 964239, 1660748, 2783499, 4550843, 7273394, 11385571, 17485634, 26385946, 39175444, 57296576, 82639259, 117654736, 165492559

Offset: 5

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

A column of triangle A026998.

Programs

GAP

a:=[1, 4, 11, 29, 76, 199, 518, 1324, 3278, 7784, 17643];; for n in [12..40] do a[n]:=11*a[n-1]-55*a[n-2]+165*a[n-3]-330*a[n-4]+462*a[n-5] -462*a[n-6]+330*a[n-7]-165*a[n-8]+55*a[n-9]-11*a[n-10]+a[n-11]; od; a; # G. C. Greubel, Sep 26 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^5*(1- 7*x+22*x^2-37*x^3+32*x^4+x^5-32*x^6+37*x^7-22*x^8+7*x^9 -x^10)/(1-x)^11 )); // G. C. Greubel, Sep 26 2019

Maple

seq(coeff(series(x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11, x, n+1), x, n), n = 5..40); # G. C. Greubel, Sep 26 2019

Mathematica

Drop[CoefficientList[Series[x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11, {x, 0, 40}], x], 5] (* G. C. Greubel, Sep 26 2019 *)

PARI

my(x='x+O('x^40)); Vec(x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11) \\ G. C. Greubel, Sep 26 2019

Sage

def A027972_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11 ).list()
a=A027972_list(40); a[5:] # G. C. Greubel, Sep 26 2019

Formula

Sequence satisfies a 10-degree polynomial approximating A002878.

G.f.: x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11. - R. J. Mathar, Jan 30 2011

a(n) = -76 +183941*n/2520 +386899*n^3/36288 -1747657*n^2/50400 -831241*n^4/362880 +11887*n^5/34560 -5807*n^6/172800 +41*n^7/24192 +n^8/60480 -n^9/145152 +n^10/3628800. - R. J. Mathar, Jan 30 2011