A160282 Numerator of Hermite(n, 20/29).

1, 40, -82, -137840, -5099828, 723394400, 71825329480, -4427483105600, -1022770753521520, 18665382528092800, 16229318967932481760, 335221024594778374400, -286866018560895642547520, -18240741902856832410790400, 5542982685738270823512456320

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..372

Formula

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 29^n * Hermite(n, 20/29).

E.g.f.: exp(40*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 40/29, -82/841, -137840/24389, -5099828/707281, ...

Mathematica

Table[29^n*HermiteH[n, 20/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 20/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A069070 A174052 A141528 * A243803 A203855 A188335

Adjacent sequences: A160279 A160280 A160281 * A160283 A160284 A160285

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved