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

%I

%S 1,2,1,8,2,2,16,8,4,6,128,16,16,4,24,256,128,32,16,48,120,1024,256,

%T 256,32,192,240,720,2048,1024,512,256,384,64,96,5040,32768,2048,2048,

%U 512,3072,384,384,10080,40320,65536,32768,4096,2048,6144,3072,2304,40320

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

%C The corresponding numerator table is given in A131440.

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 775, 22.3.9.

%H Wolfdieter Lang, <a href="/A130562/a130562.txt">Rational coefficients and more</a>

%F 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).

%e Triangle begins:

%e [1];

%e [2,1];

%e [8,2,2];

%e [16,8,4,6];

%e [128,16,16,4,24];

%e [256,128,32,16,48,120];

%e ...

%o (Python)

%o from sympy import binomial, factorial, Integer

%o def a(n, m): return ((-1)**m * binomial(n + 1/Integer(2), n -m) / factorial(m)).denominator()

%o for n in range(21): print([a(n, m) for m in range(n + 1)]) # _Indranil Ghosh_, Jun 29 2017

%Y Cf. A021009 (Coefficient table of n!*L(n, 0, x).

%K nonn,tabl,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 13 2007

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