A159545 Numerator of Hermite(n, 1/18).

1, 1, -161, -485, 77761, 392041, -62594369, -443658221, 70538356225, 645519410641, -102199403965409, -1147940849203829, 180971397017155009, 2412568407869398585, -378713193710259050369, -5850418342758055041149, 914422642373171437355521

Offset

0,3

Links

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

Formula

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 9^n * Hermite(n,1/18).

E.g.f.: exp(x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 1/18], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/18)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Crossrefs

Cf. A159542, A159543, A159544.

Sequence in context: A209282 A340241 A157954 * A157337 A200869 A200883

Adjacent sequences: A159542 A159543 A159544 * A159546 A159547 A159548

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved