A159645 Numerator of Hermite(n, 7/19).

1, 14, -526, -27580, 753196, 90195784, -1456296584, -411116288464, 1604494897040, 2397070610726624, 23132980709206816, -16982988079517329856, -421483965905763150656, 141239833198257461763200, 5933406168767097396742016, -1344584547605247059948037376

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..396

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 19^n * Hermite(n, 7/19).

E.g.f.: exp(14*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 7/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 7/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/19)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/19)^(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, A159644.

Sequence in context: A344114 A233014 A209096 * A297805 A326331 A210029

Adjacent sequences: A159642 A159643 A159644 * A159646 A159647 A159648

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved