A159546 Numerator of Hermite(n, 5/18).

1, 5, -137, -2305, 55057, 1768925, -35751545, -1898152825, 31051487905, 2615263500725, -32196751861865, -4397710630483825, 35386058665424305, 8726079758987677325, -30892640754445199705, -19945212097156278171625, -24656943452479555574975

Offset

0,2

Links

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

Formula

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

a(n) = 9^n * Hermite(n,5/18).

E.g.f.: exp(5*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 5/18], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/18)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018

Crossrefs

Cf. A159545.

Sequence in context: A279307 A265875 A248523 * A339566 A012215 A012142

Adjacent sequences: A159543 A159544 A159545 * A159547 A159548 A159549

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved