A130562 Triangular table of denominators of the coefficients of Laguerre-Sonin polynomials L(1/2,n,x).

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

Table of n, a(n) for n=0..52.

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.

Wolfdieter Lang, Rational coefficients and more

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

Adjacent sequences: A130559 A130560 A130561 * A130563 A130564 A130565

Keyword

nonn,tabl,frac,easy

Author

Wolfdieter Lang, Jul 13 2007

Status

approved