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a(n) = 2 * A000538(n).
4

%I #29 Oct 04 2024 00:22:35

%S 0,2,34,196,708,1958,4550,9352,17544,30666,50666,79948,121420,178542,

%T 255374,356624,487696,654738,864690,1125332,1445332,1834294,2302806,

%U 2862488,3526040,4307290,5221242,6284124,7513436,8927998,10547998,12395040,14492192,16864034,19536706

%N a(n) = 2 * A000538(n).

%H Colin Barker, <a href="/A259108/b259108.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. See p. 357.

%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_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = -n/15+(2*n^3)/3+n^4+(2*n^5)/5. - _Colin Barker_, Jun 28 2015

%F G.f.: 2*x*(x+1)*(x^2+10*x+1) / (x-1)^6. - _Colin Barker_, Jun 28 2015

%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - _Wesley Ivan Hurt_, Oct 01 2021

%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,2,34,196,708,1958},40] (* _Harvey P. Dale_, Aug 16 2018 *)

%o (PARI) concat(0, Vec(2*x*(x+1)*(x^2+10*x+1)/(x-1)^6 + O(x^100))) \\ _Colin Barker_, Jun 28 2015

%o (Python)

%o def A259108(n): return n*(n**2*(n*(3*(2*n+5))+10)-1)//15 # _Chai Wah Wu_, Oct 03 2024

%Y Cf. A000538.

%K nonn,easy

%O 0,2

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