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%I #26 Mar 25 2022 03:01:20
%S 4,35,100,210,380,627,970,1430,2030,2795,3752,4930,6360,8075,10110,
%T 12502,15290,18515,22220,26450,31252,36675,42770,49590,57190,65627,
%U 74960,85250,96560,108955,122502,137270,153330,170755,189620,210002,231980,255635,281050,308310
%N Expansion of (4 + 15*x - 35*x^2 + 20*x^3 - 2*x^5)/(1 - x)^5.
%H Colin Barker, <a href="/A257600/b257600.txt">Table of n, a(n) for n = 0..1000</a>
%H Yang-Hui He and John McKay, <a href="http://arxiv.org/abs/1505.06742">Sporadic and Exceptional</a>, arXiv:1505.06742 [math.AG], 2015.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (24 + 250*n + 125*n^2 + 20*n^3 + n^4)/12 for n > 0. - _Colin Barker_, Apr 15 2016
%F From _G. C. Greubel_, Mar 24 2022: (Start)
%F a(n) = 2*[n=0] + A257601(n).
%F E.g.f.: 2 + (1/12)*(24 + 396*x + 192*x^2 + 26*x^3 + x^4)*exp(x). (End)
%t CoefficientList[Series[(4 +15x -35x^2 +20x^3 -2x^5)/(1-x)^5, {x,0,50}], x] (* _Vincenzo Librandi_, Jun 08 2015
%o (Magma) I:=[4,35,100,210,380,627]; [n le 6 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..51]]; // _Vincenzo Librandi_, Jun 08 2015
%o (PARI) Vec((4+15*x-35*x^2+20*x^3-2*x^5)/(1-x)^5 + O(x^50)) \\ _Colin Barker_, Apr 15 2016
%o (Sage) [2*bool(n==0) + (24+250*n+125*n^2+20*n^3+n^4)/12 for n in (0..50)] # _G. C. Greubel_, Mar 24 2022
%Y Agrees with A257601 except for first term.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Jun 07 2015
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