A160237 Numerator of Hermite(n, 6/29).

1, 12, -1538, -58824, 7054860, 480426192, -53566258296, -5491256229216, 564794050426512, 80667872425448640, -7581837866251154976, -1447815668591059984512, 122905376178286149551808, 30697575968981388522011904, -2319078043886628283835690880

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..371

Formula

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

a(n) = 29^n * Hermite(n, 6/29).

E.g.f.: exp(12*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 12/29, -1538/841, -58824/24389, 7054860/707281,...

Mathematica

Table[29^n*HermiteH[n, 6/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 6/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/29)^(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. A009973 (denominators).

Sequence in context: A271434 A299694 A366832 * A013474 A013515 A159383

Adjacent sequences: A160234 A160235 A160236 * A160238 A160239 A160240

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved