A160288 Numerator of Hermite(n, 26/29).

1, 52, 1022, -121784, -11489780, 221894192, 108167547784, 3385356299104, -1097526180055408, -102624715723624640, 11277866096050285024, 2312596755465981266048, -88408047224891347679552, -51274671368019715953249536, -733152550517551021207891840

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, 26/29).

E.g.f.: exp(52*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 52/29, 1022/841, -121784/24389, -11489780/707281, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 26/29]] (* Harvey P. Dale, Nov 24 2017 *)
Table[29^n*HermiteH[n, 26/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 26/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(52*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(52/29)^(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: A278001 A083936 A273655 * A133238 A331127 A216939

Adjacent sequences: A160285 A160286 A160287 * A160289 A160290 A160291

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved