A160004 Numerator of Hermite(n, 2/25).

1, 4, -1234, -14936, 4567756, 92951024, -28176670904, -809839363616, 243306512955536, 9071619687982144, -2700911791997851424, -124198893267768205696, 36640741566899384257216, 2009546365284120622468864, -587373865000978511689884544, -37516556852476024939964658176

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..380

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 25^n * Hermite(n, 2/25).

E.g.f.: exp(4*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 4/25, -1234/625, -14936/15625, 4567756/390625, ...

Mathematica

Numerator[Table[HermiteH[n, 2/25], {n, 0, 30}]] (* G. C. Greubel, Jul 16 2018 *)
(* Alternative: *)
Table[25^n* HermiteH[n, 2/25], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 625*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A198899 A350341 A253168 * A324299 A227850 A384206

Adjacent sequences: A160001 A160002 A160003 * A160005 A160006 A160007

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved