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URL: https://oeis.org/A159647

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A159647
Numerator of Hermite(n, 9/19).
1
1, 18, -398, -33156, 265260, 100529208, 851937144, -420157660464, -11868528214128, 2213197138985760, 116959244837147424, -13874016936408533568, -1178622627351978445632, 98989275444707922811776, 12844358938330412301313920, -769385135305160262357781248
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 19^n * Hermite(n, 9/19).
E.g.f.: exp(18*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
MATHEMATICA
Numerator[Table[HermiteH[n, 9/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 9/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 9/19)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/19)^(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
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved