A160151 Numerator of Hermite(n, 23/27).

1, 46, 658, -103868, -7656020, 253581256, 67477123576, 885618857008, -647933055794288, -40134778914678560, 6655977728057433376, 891340052066655340096, -65746928407518970839872, -18619244257704074488953728, 389682045181727146807062400

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..376

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 23/27).

E.g.f.: exp(46*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 46/27, 658/729, -103868/19683, -7656020/531441, ...

Mathematica

Table[27^n*HermiteH[n, 23/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
HermiteH[Range[0, 20], 23/27]//Numerator (* Harvey P. Dale, Jan 02 2019 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(46/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Crossrefs

Cf. A009971 (denominators).

Sequence in context: A098227 A077732 A200898 * A278204 A223929 A224053

Adjacent sequences: A160148 A160149 A160150 * A160152 A160153 A160154

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved