A159240 Numerator of Hermite(n, 5/9).

1, 10, -62, -3860, -8468, 2416600, 31025080, -2038684400, -55569284720, 2086442135200, 101884438473760, -2361191874286400, -205169988103104320, 2538457122581718400, 457472566170954881920, -1182495092305788512000, -1123483286718478248185600

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jun 28 2018: (Start)

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

E.g.f.: exp(10*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 5/9], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/9)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018

Crossrefs

Cf. A159030, A159197.

Sequence in context: A289799 A027254 A370764 * A268945 A055368 A278802

Adjacent sequences: A159237 A159238 A159239 * A159241 A159242 A159243

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved