A160259 Numerator of Hermite(n, 11/29).

1, 22, -1198, -100364, 3837100, 759665192, -15557376776, -8008803406736, 6978879212432, 107919993983713120, 2268593594123893024, -1765305239735329031872, -80810233952657507431232, 33853095811859416015817344, 2511764683469716209839300480

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, 11/29).

E.g.f.: exp(22*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 22/29, -1198/841, -100364/24389, 3837100/707281,...

Mathematica

Table[29^n*HermiteH[n, 11/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0, 20], 11/29]//Numerator (* Harvey P. Dale, Mar 18 2023 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/29)^(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: A209728 A319667 A038695 * A055475 A348813 A160309

Adjacent sequences: A160256 A160257 A160258 * A160260 A160261 A160262

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved