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A159682
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Numerator of Hermite(n, 19/20).
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1
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1, 19, 161, -4541, -182879, 158099, 185882881, 3342055939, -196736970559, -9085291943021, 181506000088801, 21619197887729219, 11451559671492961, -51668495296791759341, -1011475465784925126079, 125453752981103348759299, 5418047703995739004663681
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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) -19*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 17 2014
a(n) = 10^n * Hermite(n,19/20).
E.g.f.: exp(19*x-100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/20)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 19/10, 161/100, -4541/1000, -182879/10000, 158099/100000,..
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MAPLE
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orthopoly[H](n, 19/20) ;
numer(%) ;
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MATHEMATICA
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/20)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 02 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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