A160222 Numerator of Hermite(n, 25/28).

1, 25, 233, -13775, -618383, 6139625, 1365521305, 19697634625, -3254549595295, -143135522066375, 7903662920541385, 758682819513724625, -15113524025531336495, -3946682083630844048375, -21648533656663410430855, 21118177933549486876710625

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..417

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 14^n * Hermite(n, 25/28).

E.g.f.: exp(25*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(25/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 25/14, 233/196, -13775/2744, -618383/38416

Mathematica

Table[14^n*HermiteH[n, 25/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 25/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(25*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(25/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Crossrefs

Cf. A001023 (denominators).

Sequence in context: A053927 A081195 A221930 * A088890 A108178 A278849

Adjacent sequences: A160219 A160220 A160221 * A160223 A160224 A160225

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved