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A027971
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T(n, 2n-9), T given by A027960.
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3
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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
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OFFSET
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5,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
(Magma) R<x>:=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
(Sage)
P.<x> = 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()
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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