A159247 Numerator of Hermite(n, 1/10).

1, 1, -49, -149, 7201, 37001, -1763249, -12863549, 604273601, 5749693201, -266173427249, -3141020027749, 143254364959201, 2027866381608601, -91087470841872049, -1510593937967892749, 66805009193436144001, 1275280159567750343201, -55508977654852972057649

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..450 (terms 0..100 from T. D. Noe)

Formula

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

a(n) = 5^n * Hermite(n,1/10).

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

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

a(n) = 50*(1-n)*a(n-2)+a(n-1) for n>1. - Christian Krause, Oct 21 2024

Mathematica

Numerator[Table[HermiteH[n, 1/10], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/10)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/5)^(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. A158811, A158954, A158960.

Sequence in context: A027469 A044381 A044762 * A265423 A226146 A339730

Adjacent sequences: A159244 A159245 A159246 * A159248 A159249 A159250

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved