A070781 - OEIS

%I #24 Apr 08 2022 11:13:19

%S 1,4,126,11440,2042975,600805296,262596783764,159518999862720,

%T 128447994798305325,132341572939212267400,169758547725351091518726,

%U 265242021590899282966358400,495874093230232452749553398586,1092844289151775603486607296657120

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

%C 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

%H T. D. Noe, <a href="/A070781/b070781.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = binomial((n+1)^2, 2*n+1). - _Gleb Ivanov_, Mar 15 2022

%t Binomial[#[[2]],#[[1]]]&/@Partition[Range[0,20]^2,2,1] (* _Harvey P. Dale_, Jul 29 2015 *)

%Y Cf. A007318.

%K nonn

%O 0,2

%A _Karol A. Penson_, May 06 2002

%E Better definition from _Amarnath Murthy_, Jul 14 2005

%E a(13) from _Harvey P. Dale_, Jul 29 2015