A159621 Numerator of Hermite(n, 4/19).

1, 8, -658, -16816, 1290700, 58890208, -4188305336, -288618823744, 18858744578192, 1817932282570880, -108000664008524576, -13989476392229950208, 745825462417862580928, 127171427161623189249536, -5982946372961072670593920, -1333312356733375778299061248

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, 4/19).

E.g.f.: exp(8*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 4/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 4/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/19)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/19)^(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.

Sequence in context: A235368 A247731 A231849 * A015106 A099126 A172919

Adjacent sequences: A159618 A159619 A159620 * A159622 A159623 A159624

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved