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A027933 a(n) = T(n, 2*n-10), T given by A027926. 3
1, 2, 5, 13, 34, 89, 232, 596, 1490, 3588, 8273, 18228, 38403, 77533, 150438, 281403, 509015, 892926, 1523117, 2532359, 4112704, 6536993, 10186540, 15586342, 23449376, 34731776, 50700937, 73018870, 103843433, 145950389, 202879594, 279108997, 380260541 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Colin Barker, 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

a(n) = Sum_{k=0..5} binomial(n-k, 10-2*k). - Len Smiley, Oct 20 2001

a(n) = 34 -9161*n/280 -101897*n^3/20160 +794293*n^2/50400 -287*n^5/1280 +438209*n^4/362880 +5593*n^6/172800 -47*n^7/13440 -n^9/80640 +n^8/3780 +n^10/3628800. - R. J. Mathar, Oct 05 2009

G.f.: x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11. - Colin Barker, Feb 17 2016

MAPLE

seq(add(binomial(n-k, 10-2*k), k=0..5), n=5..40); # G. C. Greubel, Sep 27 2019

MATHEMATICA

Table[Sum[Binomial[n-k, 10-2k], {k, 0, 5}], {n, 5, 40}] (* or *)

Drop[#, 5] &@ CoefficientList[Series[x^5(1-x+x^2)(1-5x+9x^2-5x^3+x^4)(1- 3x+5x^2-3x^3+x^4)/(1-x)^11, {x, 0, 37}], x] (* Michael De Vlieger, Feb 17 2016 *)

PROG

(PARI) Vec(x^5*(1-x+x^2)*(1-5*x+9*x^2-5*x^3+x^4)*(1-3*x+5*x^2-3*x^3+x^4) / (1-x)^11 + O(x^40)) \\ Colin Barker, Feb 17 2016

(PARI) vector(40, n, sum(k=0, 5, binomial(n+4-k, 10-2*k)) ) \\ G. C. Greubel, Sep 27 2019

(MAGMA) [&+[Binomial(n-k, 10-2*k): k in [0..5]] : n in [5..40]]; // G. C. Greubel, Sep 27 2019

(Sage) [sum(binomial(n-k, 10-2*k) for k in (0..5)) for n in (5..40)] # G. C. Greubel, Sep 27 2019

(GAP) List([5..40], n-> Sum([0..5], k-> Binomial(n-k, 10-2*k)) ); # G. C. Greubel, Sep 27 2019

CROSSREFS

Cf. A027926, A228074.

Sequence in context: A209230 A103142 A112844 * A141448 A011783 A001519

Adjacent sequences:  A027930 A027931 A027932 * A027934 A027935 A027936

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)