A160281 Numerator of Hermite(n, 19/29).

1, 38, -238, -136876, -4000340, 768888808, 62860634104, -5370921754384, -944216132607088, 36390910087921760, 15676398398747125024, -16391968526453252288, -290667617977624530780992, -10714513990411799725496704, 5948586603063089600488296320

Offset

0,2

Links

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

Formula

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

a(n) = 29^n * Hermite(n, 19/29).

E.g.f.: exp(38*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 38/29, -238/841, -136876/24389, -4000340/707281, ...

Mathematica

Table[29^n*HermiteH[n, 19/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/29)^(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: A259518 A209250 A165068 * A186119 A007229 A367968

Adjacent sequences: A160278 A160279 A160280 * A160282 A160283 A160284

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved