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

1,2

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.

Formula

a(n) = A060543(n, n) = A014062(n)/n.

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)

Maple

A060545:=n->binomial(n^2, n)/n: seq(A060545(n), n=1..20); # Wesley Ivan Hurt, Sep 28 2016

Mathematica

Table[Binomial[n^2, n]/n, {n, 15}] (* Michael De Vlieger, Sep 28 2016 *)

Prog

(PARI) a(n) = binomial(n^2, n)/n; \\ Harry J. Smith, Jul 06 2009

Crossrefs

Cf. A005563, A014062, A060543.

Sequence in context: A319369 A340789 A210854 * A108288 A327362 A327071

Adjacent sequences: A060542 A060543 A060544 * A060546 A060547 A060548

Keyword

nonn,easy

Author

Henry Bottomley, Apr 02 2001

Extensions

More terms from Fred Daniel Kline, Sep 28 2016

Status

approved