A158903 Numerator of Hermite(n, 2/3).

1, 4, -2, -152, -500, 8944, 80776, -642848, -12749168, 41573440, 2231658976, 1443416704, -436094810432, -2056157249792, 93821556641920, 893437853515264, -21758068879257344, -344342377329425408, 5280599567735045632, 132689328525674014720, -1275207738062689547264

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 13 2018: (Start)

a(n) = 3^n * Hermite(n, 2/3).

E.g.f.: exp(4*x - 9*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/3)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 2/3], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011*)
Table[3^n*HermiteH[n, 2/3], {n, 0, 30}] (* G. C. Greubel, Jul 13 2018 *)

Prog

(PARI) a(n)=3^n*polhermite(n, 2/3) \\ Charles R Greathouse IV, Jun 19 2012
(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 9*x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 2018

Crossrefs

The denominators are A000244.

Sequence in context: A057167 A355646 A096683 * A273148 A276342 A350725

Adjacent sequences: A158900 A158901 A158902 * A158904 A158905 A158906

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved