A135861 a(n) = binomial(n*(n+1),n)/(n+1).

1, 1, 5, 55, 969, 23751, 749398, 28989675, 1329890705, 70625252863, 4263421511271, 288417894029200, 21616536107173175, 1778197364075525550, 159297460456229992380, 15438280311293473537331, 1609484153977526457766689, 179612918129148904884024975

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..338

R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011.

Formula

a(n) = A135860(n)/(n+1).

a(n) = [x^(n^2)] 1/(1 - x)^n. - Ilya Gutkovskiy, Oct 10 2017

a(p) == 1 ( mod p^4 ) for prime p >= 5 and a(2*p) == 4*p + 1 ( mod p^4 ) for prime p >= 5 (apply Mestrovic, equation 37). - Peter Bala, Feb 23 2020

a(n) ~ exp(n + 1/2) * n^(n - 3/2) / sqrt(2*Pi). - Vaclav Kotesovec, Oct 17 2020

Maple

A135861:=n->binomial(n*(n+1), n)/(n+1); seq(A135861(n), n=0..15); # Wesley Ivan Hurt, May 08 2014

Mathematica

Table[Binomial[n*(n + 1), n]/(n + 1), {n, 0, 15}]

Prog

(PARI) a(n)=binomial(n*(n+1), n)/(n+1)

Crossrefs

Cf. A014068, A107863, A135860, A135862, A295763.

Sequence in context: A195513 A172493 A155807 * A141361 A203013 A266481

Adjacent sequences: A135858 A135859 A135860 * A135862 A135863 A135864

Keyword

nonn

Author

Paul D. Hanna, Dec 02 2007

Status

approved