A160220 Numerator of Hermite(n, 19/28).

1, 19, -31, -15485, -257759, 19383059, 873485761, -28992725309, -2947706709055, 34914759096979, 11062889692388641, 73329048495226499, -46309928432170516511, -1224828484332785265005, 212723654088018032104961, 10763608149690668144341699, -1046306531193423334034678399

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, 19/28).

E.g.f.: exp(19*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 19/14, -31/196, -15485/2744, -257759/38416

Mathematica

Numerator[HermiteH[Range[0, 20], 19/28]] (* Harvey P. Dale, Jul 26 2015 *)
Table[14^n*HermiteH[n, 19/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/14)^(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: A147210 A146816 A146659 * A133151 A184750 A101063

Adjacent sequences: A160217 A160218 A160219 * A160221 A160222 A160223

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved