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A257601 a(n) = (n^4 + 20*n^3 + 125*n^2 + 250*n + 24)/12. 2

%I #26 Mar 25 2022 03:02:01

%S 2,35,100,210,380,627,970,1430,2030,2795,3752,4930,6360,8075,10110,

%T 12502,15290,18515,22220,26450,31252,36675,42770,49590,57190,65627,

%U 74960,85250,96560,108955,122502,137270,153330,170755,189620,210002,231980,255635,281050,308310,337502

%N a(n) = (n^4 + 20*n^3 + 125*n^2 + 250*n + 24)/12.

%H G. C. Greubel, <a href="/A257601/b257601.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 G.f.: (2 + 25*x - 55*x^2 + 40*x^3 - 10*x^4)/(1-x)^5. - _Vincenzo Librandi_, Jun 08 2015

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Vincenzo Librandi_, Jun 08 2015

%F E.g.f.: (1/12)*(24 + 396*x + 192*x^2 + 26*x^3 + x^4)*exp(x). - _G. C. Greubel_, Mar 24 2022

%t Table[(n^4 +20*n^3 +125*n^2 +250*n +24)/12, {n, 0, 50] (* _Bruno Berselli_, Jun 08 2015 *)

%t LinearRecurrence[{5,-10,10,-5,1},{2,35,100,210,380},50] (* _Harvey P. Dale_, Oct 21 2018 *)

%o (Sage) [(n^4 +20*n^3 +125*n^2 +250*n +24)/12 for n in (0..50)] # _Bruno Berselli_, Jun 08 2015

%o (Magma) I:=[2,35,100,210,380]; [n le 5 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..45]]; // _Vincenzo Librandi_, Jun 08 2015

%Y Agrees with A257600 except for first term.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Jun 07 2015

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)