A158967 Numerator of Hermite(n, 4/5).

1, 8, 14, -688, -7604, 76768, 2515144, -2909248, -903574384, -6064895872, 358089305824, 5897162382592, -149771819142464, -4736471982694912, 59459906581042304, 3791209640534776832, -14265252811503513344, -3147089734919849572352

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

DLMF, Digital library of mathematical functions, Table 18.9.1 for H_n(x).

Formula

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

a(n) = 5^n * Hermite(n, 4/5).

E.g.f.: exp(8*x - 25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -8*a(n-1) +50*(n-1)*a(n-2)=0. - [DLMF] Georg Fischer, Feb 06 2021

Mathematica

Numerator[Table[HermiteH[n, 4/5], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[5^n*HermiteH[n, 4/5], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/5)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 25*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 2018

Crossrefs

Cf. A158960, A158961.

Sequence in context: A180756 A279708 A327875 * A253287 A357514 A331814

Adjacent sequences: A158964 A158965 A158966 * A158968 A158969 A158970

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved