OFFSET
0,2
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).
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
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 2, 34, 196, 708, 1958}, 40] (* Harvey P. Dale, Aug 16 2018 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 24 2015
STATUS
approved