A070781 a(n) = binomial((n+1)^2, n^2).

1, 4, 126, 11440, 2042975, 600805296, 262596783764, 159518999862720, 128447994798305325, 132341572939212267400, 169758547725351091518726, 265242021590899282966358400, 495874093230232452749553398586, 1092844289151775603486607296657120

Offset

0,2

Comments

All primes between n^2 and (n+1)^2 divide a(n). No prime between (n+1)^2/2 and n^2 divides a(n). Every prime greater than n+1 has exponent 0 or 1 in the prime factorization of a(n). - T. D. Noe, Aug 09 2008

Links

T. D. Noe, Table of n, a(n) for n = 0..50

Formula

a(n) = binomial((n+1)^2, 2*n+1). - Gleb Ivanov, Mar 15 2022

Mathematica

Binomial[#[[2]], #[[1]]]&/@Partition[Range[0, 20]^2, 2, 1] (* Harvey P. Dale, Jul 29 2015 *)

Crossrefs

Cf. A007318.

Sequence in context: A178842 A054053 A348814 * A152421 A270959 A291851

Adjacent sequences: A070778 A070779 A070780 * A070782 A070783 A070784

Keyword

nonn

Author

Karol A. Penson, May 06 2002

Extensions

Better definition from Amarnath Murthy, Jul 14 2005

a(13) from Harvey P. Dale, Jul 29 2015

Status

approved