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A130562
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Triangular table of denominators of the coefficients of Laguerre-Sonin polynomials L(1/2,n,x).
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2
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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
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OFFSET
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0,2
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COMMENTS
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The corresponding numerator table is given in A131440.
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LINKS
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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].
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FORMULA
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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).
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EXAMPLE
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Triangle begins:
[1];
[2,1];
[8,2,2];
[16,8,4,6];
[128,16,16,4,24];
[256,128,32,16,48,120];
...
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PROG
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(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
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CROSSREFS
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Cf. A021009 (Coefficient table of n!*L(n, 0, x).
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KEYWORD
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AUTHOR
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STATUS
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approved
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