A159647 Numerator of Hermite(n, 9/19).

1, 18, -398, -33156, 265260, 100529208, 851937144, -420157660464, -11868528214128, 2213197138985760, 116959244837147424, -13874016936408533568, -1178622627351978445632, 98989275444707922811776, 12844358938330412301313920, -769385135305160262357781248

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..397

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

Cf. A159564, A159618, A159646.

Sequence in context: A324431 A070943 A252888 * A111454 A116421 A298465

Adjacent sequences: A159644 A159645 A159646 * A159648 A159649 A159650

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved