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A130562
Triangular table of denominators of the coefficients of Laguerre-Sonin polynomials L(1/2,n,x).
2
1, 2, 1, 8, 2, 2, 16, 8, 4, 6, 128, 16, 16, 4, 24, 256, 128, 32, 16, 48, 120, 1024, 256, 256, 32, 192, 240, 720, 2048, 1024, 512, 256, 384, 64, 96, 5040, 32768, 2048, 2048, 512, 3072, 384, 384, 10080, 40320, 65536, 32768, 4096, 2048, 6144, 3072, 2304, 40320
OFFSET
0,2
COMMENTS
The corresponding numerator table is given in A131440.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 775, 22.3.9.
FORMULA
a(n,m) = denom(L(1/2,n,m)) with L(1/2,n,m)=((-1)^m)*binomial(n+1/2,n-m)/m!, n>=m>=0, else 0 (taken in lowest terms).
EXAMPLE
Triangle begins:
1;
2, 1;
8, 2, 2;
16, 8, 4, 6;
128, 16, 16, 4, 24;
256, 128, 32, 16, 48, 120;
...
PROG
(Python)
from sympy import binomial, factorial, Integer
def a(n, m): return ((-1)**m * binomial(n + 1/Integer(2), n -m) / factorial(m)).denominator()
for n in range(21): print([a(n, m) for m in range(n + 1)]) # Indranil Ghosh, Jun 29 2017
CROSSREFS
Cf. A021009 (Coefficient table of n!*L(n, 0, x)).
Sequence in context: A046740 A317932 A253583 * A363894 A152250 A154175
KEYWORD
nonn,tabl,frac,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved