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A158968
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Numerator of Hermite(n, 1/6).
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2
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1, 1, -17, -53, 865, 4681, -73169, -578717, 8640577, 91975825, -1307797649, -17863446149, 241080488353, 4099584856537, -52313249418065, -1085408633265389, 13039168709612161, 325636855090044193, -3664348770051277073, -109170689819225595605, 1144036589538311163361
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 3^n * Hermite(n, 1/6).
E.g.f.: exp(x - 9*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -a(n-1) +18*(n-1)*a(n-2)=0. - [DLMF] Georg Fischer, Feb 06 2021
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MATHEMATICA
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Table[3^n*HermiteH[n, 1/6], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 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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