A094323 - OEIS

A094323

a(n) = n*(n+1)*(2n+1)*(3n+1)*(4n+1)/30.

0, 4, 63, 364, 1326, 3696, 8645, 17864, 33660, 59052, 97867, 154836, 235690, 347256, 497553, 695888, 952952, 1280916, 1693527, 2206204, 2836134, 3602368, 4525917, 5629848, 6939380, 8481980, 10287459, 12388068, 14818594, 17616456, 20821801, 24477600, 28629744

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..32.

FORMULA

From Amiram Eldar, Mar 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 300 + (135*sqrt(3)/2 - 160)*Pi - 1200*log(2) + 1215*log(3)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (60 + 160*sqrt(2) - 135*sqrt(3))*Pi + (160*sqrt(2) - 380)*log(2) - 320*sqrt(2)*log(2-sqrt(2)) - 300. (End)

EXAMPLE

a(4) = 4*5*9*13*17/30 = 1326.

MATHEMATICA