login
3

%I #17 Mar 05 2022 03:56:10

%S 0,2,20,70,168,330,572,910,1360,1938,2660,3542,4600,5850,7308,8990,

%T 10912,13090,15540,18278,21320,24682,28380,32430,36848,41650,46852,

%U 52470,58520,65018,71980,79422,87360,95810,104788,114310,124392,135050,146300,158158,170640,183762,197540,211990,227128,242970

%N 2*A000447(n).

%H Colin Barker, <a href="/A259110/b259110.txt">Table of n, a(n) for n = 0..1000</a>

%H J. L. Bailey, Jr., <a href="http://dx.doi.org/10.1214/aoms/1177732978">A table to facilitate the fitting of certain logistic curves</a>, Annals Math. Stat., 2 (1931), 355-359.

%H J. L. Bailey, <a href="/A002309/a002309.pdf">A table to facilitate the fitting of certain logistic curves</a>, Annals Math. Stat., 2 (1931), 355-359. [Annotated scanned copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (2*n*(4*n^2-1))/3. - _Colin Barker_, Jun 28 2015

%F G.f.: 2*x*(x^2+6*x+1) / (x-1)^4. - _Colin Barker_, Jun 28 2015

%F a(n) = 2*binomial(2*n+1, 3). - _Michel Marcus_, Mar 05 2022

%t LinearRecurrence[{4,-6,4,-1},{0,2,20,70},50] (* _Harvey P. Dale_, Feb 01 2018 *)

%o (PARI) concat(0, Vec(2*x*(x^2+6*x+1)/(x-1)^4 + O(x^100))) \\ _Colin Barker_, Jun 28 2015

%Y Cf. A000447.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jun 24 2015