A159644 Numerator of Hermite(n, 6/19).

1, 12, -578, -24264, 960780, 81603792, -2489170296, -383377670496, 7979734630032, 2310146240345280, -24130560741804576, -16968822584194576512, -11980957598922975552, 146874107378274735193344, 1874942556562787870851200, -1462104166700847568884106752

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 10 2018: (Start)

a(n) = 19^n * Hermite(n, 6/19).

E.g.f.: exp(12*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 6/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 6/19], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 6/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/19)^(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

Crossrefs

Cf. A159564, A159618.

Sequence in context: A159722 A307948 A042111 * A217390 A219103 A219982

Adjacent sequences: A159641 A159642 A159643 * A159645 A159646 A159647

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved