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A159620
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Numerator of Hermite(n, 3/19).
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1
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1, 6, -686, -12780, 1409196, 45363816, -4815014664, -225406138896, 22982647278480, 1439841741934176, -140702191563957984, -11239870526148498624, 1050017582244063317184, 103682343732014971981440, -9233370964550688463200384, -1103421356230511467567597824
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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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a(n) = 19^n * Hermite(n, 3/19).
E.g.f.: exp(6*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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MATHEMATICA
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Table[19^n*HermiteH[n, 3/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(6*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 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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