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