A108214 Denominator of the O(x^2) term in the Maclaurin series of the square of the Jacobi polynomial P^{a,b}_n(z) about z=1-x for real positive x.

8, 48, 576, 11520, 345600, 14515200, 812851200, 58525286400, 5267275776000, 579400335360000, 76480844267520000, 11931011705733120000, 2171444130443427840000, 456003267393119846400000

Offset

2,1

Comments

The sequence starts at n=2 because the n=1 and n=0 terms are not quadratic in x and the denominator of 0 is undefined.

This sequence arises out of my preliminary investigation into the square-summability of the Jacobi polynomials, i.e., does Sum_{n=0}^ infinity {P^{a,b}_n(z)}^2 exist?

References

N. N. Lebedev & Richard A. Silverman (translator), Special Functions & their Applications, Dover Publications, New York, 1972, pp. 96-97.

Links

Table of n, a(n) for n=2..15.

Formula

a(n) = 4*(n-1)!*n!.

Mathematica

Table[4(n-1)!(n)!, {n, 2, 16}] (* for the first 14 terms *)

Crossrefs

Sequence in context: A222382 A220802 A052575 * A249514 A279739 A181276

Adjacent sequences: A108211 A108212 A108213 * A108215 A108216 A108217

Keyword

frac,easy,nonn

Author

Graham L. Giller (graham(AT)gillerinvestments.com), Jun 16 2005

Status

approved