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A158811
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Numerator of Hermite(n, 1/3).
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6
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1, 2, -14, -100, 556, 8312, -33416, -964528, 2281360, 143454752, -82670816, -25987196992, -35605572416, 5542023405440, 19415750756224, -1357758396658432, -7957769497497344, 375118879242633728, 3185315224719454720, -115167886425174418432, -1319713579704402351104
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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) -2*a(n-1) +18*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 3^n * Hermite(n,1/3).
E.g.f.: exp(2*x-9*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 2/3, -14/9, -100/27, 556/81, 8312/243, -33416/729, -964528/2187, 2281360/6561, 143454752/19683, -82670816/59049,...
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MAPLE
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orthopoly[H](n, 1/3) ;
numer(%) ;
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MATHEMATICA
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 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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