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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.
0
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.
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
KEYWORD
frac,easy,nonn
AUTHOR
Graham L. Giller (graham(AT)gillerinvestments.com), Jun 16 2005
STATUS
approved