A128542 a(n) = ((2n)^(2n) - 1)/((2n+1)*(2n-1)).

0, 1, 17, 1333, 266305, 101010101, 62350352785, 56984650387477, 72340172838076673, 121815504877079063701, 262801002506265664160401, 706890015246831381773595701, 2319540481478754999041880822337, 9120177155862455275254332279111413, 42331447143363186286810636338907542545

Offset

0,3

Comments

p divides a(p-1) for prime p>3.

Links

G. C. Greubel, Table of n, a(n) for n = 0..190

Formula

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

a(n) = A048861(2n)/((2n+1)*(2n-1)).

a(n) = A023037(2n)/(2n+1).

a(n) = A089815(2n-2).

a(n) ~ 4^(n-1) * n^(2*n-2). - Amiram Eldar, Feb 13 2026

Mathematica

Join[{0}, Table[((2n)^(2n)-1)/(4n^2-1), {n, 1, 20}]]

Prog

(PARI) A128542(n)=((n+=n)^n-1)/(n^2-1) \\ M. F. Hasler, Oct 31 2014
(Magma) [((2*n)^(2*n)-1)/(4*n^2 -1): n in [0..20]]; // G. C. Greubel, Jul 11 2019
(SageMath) [((2*n)^(2*n)-1)/(4*n^2 -1) for n in (0..20)] # G. C. Greubel, Jul 11 2019
(GAP) List([0..20], n-> ((2*n)^(2*n)-1)/(4*n^2 -1)); # G. C. Greubel, Jul 11 2019

Crossrefs

Cf. A048861 (n^n - 1).

Cf. A023037, A089815.

Sequence in context: A348598 A266866 A289945 * A316746 A396233 A067409

Adjacent sequences: A128539 A128540 A128541 * A128543 A128544 A128545

Keyword

nonn,easy

Author

Alexander Adamchuk, May 08 2007

Extensions

a(0)=0 added by M. F. Hasler, Oct 31 2014

Status

approved