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
Keywords
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.
Programs
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Maple
A135861:=n->binomial(n*(n+1),n)/(n+1); seq(A135861(n), n=0..15); # Wesley Ivan Hurt, May 08 2014
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Mathematica
Table[Binomial[n*(n + 1), n]/(n + 1), {n, 0, 15}] -
PARI
a(n)=binomial(n*(n+1),n)/(n+1)
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