OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
FORMULA
a(n) = 2F1([1-n, -n], [2], n), 2F1 the hypergeometric function.
a(n) = Sum_{j=0..n-1} ( binomial(n,j)^2*(n-j)/(j+1)*n^(j-1) ), for n>0.
a(n) ~ (sqrt(n)+1)^(2*n+1)/(2*sqrt(Pi)*(n+1/2)^(9/4)). - Peter Luschny, Nov 17 2014
MAPLE
a := n -> `if`(n=0, 1, add(binomial(n, j)^2*(n-j)/(j+1)*n^(j-1), j=0..n-1)); seq(a(n), n=0..20);
MATHEMATICA
Table[JacobiP[n, 1, -2*n-1, 1-2*n]/(n+1), {n, 0, 20}]
PROG
(Sage)
def A242369(n): return 1 if n==0 else sum( binomial(n, j)^2*(n-j)*n^(j-1)/(j+1) for j in [0..n-1])
[A242369(n) for n in [0..20]] # G. C. Greubel, Feb 16 2021
(Magma)
A242369:= func< n | n eq 0 select 1 else (&+[Binomial(n, j)^2*(n-j)*n^(j-1)/(j+1): j in [0..n-1]]) >;
[A242369(n): n in [0..30]]; // G. C. Greubel, Feb 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 08 2014
STATUS
approved