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

5,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(Sage)
def A027972_list(prec):
    P.<x> = 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
(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

Crossrefs

A column of triangle A026998.

Sequence in context: A262280 A027968 A027970 * A098149 A002878 A341341

Adjacent sequences: A027969 A027970 A027971 * A027973 A027974 A027975

Keyword

nonn

Author

Clark Kimberling

Status

approved