A259317 a(n) = 2*(2*n+1)*A000538(n) - 4*A000330(n)^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

Author

N. J. A. Sloane, Jun 24 2015

Keywords

• nonn
• easy

Examples

			n=3: 588 = 2*7*92-4*14^2.
		

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.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000538, A000330, A006331, A259108, A259109, A259318.

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,2,70,588,2772,9438,26026},30] (* Harvey P. Dale, Jul 12 2025 *)

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

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