A060545 a(n) = binomial(n^2, n)/n.
1, 3, 28, 455, 10626, 324632, 12271512, 553270671, 28987537150, 1731030945644, 116068178638776, 8634941152058949, 705873715441872264, 62895036884524942320, 6067037854078498539696, 629921975126394617164575, 70043473196734767582082230
Offset: 1
Links
- Harry J. Smith, Table of n, a(n) for n = 1..100
- Romeo Meštrović, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv preprint arXiv:1111.3057 [math.NT], 2011.
Programs
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Maple
A060545:=n->binomial(n^2,n)/n: seq(A060545(n), n=1..20); # Wesley Ivan Hurt, Sep 28 2016
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Mathematica
Table[Binomial[n^2, n]/n, {n, 15}] (* Michael De Vlieger, Sep 28 2016 *) -
PARI
a(n) = binomial(n^2, n)/n; \\ Harry J. Smith, Jul 06 2009
Formula
a(n+1) = C(A005563(n), n) for n >= 0. - Fred Daniel Kline, Sep 27 2016
From Peter Bala, Oct 22 2023: (Start)
a(p^r) == 1 (mod p^(3+r)) for all positive integers r and all primes p >= 5 (apply Meštrović, Remark 17, p. 12).
Conjecture: a(2*p^r) == 4*p^r - 1 (mod p^(3+r)) for all positive integers r and all primes p >= 5. (End)
Extensions
More terms from Fred Daniel Kline, Sep 28 2016