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A259317
a(n) = 2*(2*n+1)*A000538(n) - 4*A000330(n)^2.
2
0, 2, 70, 588, 2772, 9438, 26026, 61880, 131784, 257754, 471086, 814660, 1345500, 2137590, 3284946, 4904944, 7141904, 10170930, 14202006, 19484348, 26311012, 35023758, 46018170, 59749032, 76735960, 97569290, 122916222, 153527220, 190242668, 233999782
OFFSET
0,2
LINKS
J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359.
FORMULA
Also a(n) = (2*n+1)*A259108(n) - A006331(n)^2.
a(n) = (n*(1+2*n)^2*(-3+n+8*n^2+4*n^3))/45. - Colin Barker, Jun 28 2015
G.f.: -2*x*(x^4+28*x^3+70*x^2+28*x+1) / (x-1)^7. - Colin Barker, Jun 28 2015
EXAMPLE
n=3: 588 = 2*7*92-4*14^2.
PROG
(PARI) concat(0, Vec(-2*x*(x^4+28*x^3+70*x^2+28*x+1)/(x-1)^7 + O(x^100))) \\ Colin Barker, Jun 28 2015
(Python)
def A259317(n): return n*(n*(n**2*(n*(16*n + 48) + 40) - 11) - 3)//45 # Chai Wah Wu, Dec 07 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 24 2015
STATUS
approved