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A159460
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Numerator of Hermite(n, 9/11).
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1
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1, 18, 82, -7236, -189780, 3588408, 294225144, 85684176, -496875078768, -9109635982560, 918220473870624, 38573287607466432, -1749983724509205312, -143516534253248214144, 2922151180747492056960, 538832739303459806545152, -908419478651119648952064
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OFFSET
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0,2
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LINKS
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FORMULA
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D-finite with recurrence a(n) - 18*a(n-1) + 242*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 11^n * Hermite(n,9/11).
E.g.f.: exp(18*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 18/11, 82/121, -7236/1331, -189780/14641, 3588408/161051, ...
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MAPLE
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orthopoly[H](n, 9/11) ;
numer(%) ;
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MATHEMATICA
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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