A233446 -id:A233446 - cp's OEIS frontend

A154682 (2n-1)^(2n+1) + (2n+1)^(2n-1).

0, 4, 368, 94932, 45136576, 33739007300, 36314872537968, 53132088082450132, 101388548387203175168, 244552822542936127033092, 727457992333704231799337200, 2616052459228913777816325459284, 11187876119071565503348037263205568

Offset: 0

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 14 2009

nonn

All the terms are divisible by 4.

a(n) is divisible by (2n)^2 for n>0. a(n) = (2n)^2 * A233446(n) for n>0. - Alexander Adamchuk, Dec 10 2013

First differences of A154569. Cf. A233446.

a(n) = (2n-1)^(2n+1) + (2n+1)^(2n-1); n>=0.

A234252 a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).

Original entry on oeis.org

-1, 1, 0, 23, 112, 2637, 28928, 705259, 12021504, 337390073, 7752749056, 252186614847, 7261683740672, 271082082053317, 9359536638984192, 396049017137512403, 15920162462882529280, 754792662169555947633, 34587513064809080815616, 1818644980834260579498343

Offset: 1

Alexander Adamchuk, Dec 22 2013

sign

a(2n) = A233446(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2 = A154682(n)/(2n)^2 for n > 0.

Cf. A154682, A233446.

Table[((m-1)^(m+1)+(-1)^m*(m+1)^(m-1))/(m^2),{m,1,20}]

a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/n^2; \\ Michel Marcus, Jun 06 2021

a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).

cp's OEIS Frontend

A154682 (2n-1)^(2n+1) + (2n+1)^(2n-1).

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