A159249 Numerator of Hermite(n, 3/10).

1, 3, -41, -423, 4881, 99243, -922521, -32540463, 225260961, 13691968083, -60291528201, -7026858626103, 12079764632241, 4252354469558523, 4905216397718919, -2961932479497809343, -12564709736782617279, 2331851854387899622563, 17675558839428923554839

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 5^n * Hermite(n, 3/10).

E.g.f.: exp(3*x-25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 3/10], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/10)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/5)^(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. A159247.

Sequence in context: A280176 A322244 A181226 * A328509 A087544 A305667

Adjacent sequences: A159246 A159247 A159248 * A159250 A159251 A159252

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved