A160067 Numerator of Hermite(n, 23/25).

1, 46, 866, -75164, -6705044, 67387976, 45006371896, 1564883287216, -321821122878064, -30452604524550944, 2219667824248876576, 482762276472335122496, -8313367865694637285184, -7623849068906980152558464, -215604829352183231133449344

Offset

0,2

Links

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

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 23/25).

E.g.f.: exp(46*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 46/25, 866/625, -75164/15625, -6705044/390625, ...

Mathematica

Table[25^n*HermiteH[n, 23/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(46/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A341428 A066405 A113922 * A156842 A078427 A002138

Adjacent sequences: A160064 A160065 A160066 * A160068 A160069 A160070

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved