A242369 a(n) = P(n, 1, -2*n-1, 1-2*n)/(n+1), P the Jacobi polynomial.

1, 1, 3, 19, 185, 2426, 39907, 788019, 18130401, 475697854, 14004694451, 456820603086, 16343563014649, 636020474595988, 26736885607750515, 1207031709414024451, 58225055056545820545, 2988064457570991780854, 162517551565531508113699, 9336340704734213892357498

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

Main diagonal of A008550, A243631.

Cf. A204057.

Sequence in context: A326550 A352236 A362205 * A202617 A143633 A367180

Adjacent sequences: A242366 A242367 A242368 * A242370 A242371 A242372

Keyword

nonn

Author

Peter Luschny, Jun 08 2014

Status

approved