A259108 a(n) = 2 * A000538(n).

0, 2, 34, 196, 708, 1958, 4550, 9352, 17544, 30666, 50666, 79948, 121420, 178542, 255374, 356624, 487696, 654738, 864690, 1125332, 1445332, 1834294, 2302806, 2862488, 3526040, 4307290, 5221242, 6284124, 7513436, 8927998, 10547998, 12395040, 14492192, 16864034, 19536706

Offset: 0

Author

N. J. A. Sloane, Jun 24 2015

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359. See p. 357.
• J. L. Bailey, A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000538.

Programs

Mathematica

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

PARI

concat(0, Vec(2*x*(x+1)*(x^2+10*x+1)/(x-1)^6 + O(x^100))) \\ Colin Barker, Jun 28 2015

Python

def A259108(n): return n*(n**2*(n*(3*(2*n+5))+10)-1)//15 # Chai Wah Wu, Oct 03 2024

Formula

a(n) = -n/15+(2*n^3)/3+n^4+(2*n^5)/5. - Colin Barker, Jun 28 2015

G.f.: 2*x*(x+1)*(x^2+10*x+1) / (x-1)^6. - Colin Barker, Jun 28 2015

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