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A242369 a(n) = P(n,1,-2*n-1,1-2*n)/(n+1), P the Jacobi polynomial. 3
1, 1, 3, 19, 185, 2426, 39907, 788019, 18130401, 475697854, 14004694451, 456820603086, 16343563014649, 636020474595988, 26736885607750515, 1207031709414024451, 58225055056545820545, 2988064457570991780854, 162517551565531508113699, 9336340704734213892357498 (list; graph; refs; listen; history; text; internal format)
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..19);

MATHEMATICA

Table[JacobiP[n, 1, -2*n-1, 1-2*n]/(n+1), {n, 0, 19}]

CROSSREFS

Main diagonal of A008550, A243631.

Sequence in context: A213533 A203133 A006531 * A202617 A143633 A052888

Adjacent sequences:  A242366 A242367 A242368 * A242370 A242371 A242372

KEYWORD

nonn

AUTHOR

Peter Luschny, Jun 08 2014

STATUS

approved

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Last modified October 16 23:12 EDT 2018. Contains 316275 sequences. (Running on oeis4.)