A160289 Numerator of Hermite(n, 27/29).

1, 54, 1234, -115020, -12437844, 102210984, 110121661176, 4915056452976, -1031159390225520, -121819606703423136, 9031432087249072416, 2536703117463027057984, -30117588135278876709696, -52827165482178797480672640, -2194115753871647145822109824

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, 27/29).

E.g.f.: exp(54*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(54/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 54/29, 1234/841, -115020/24389, -12437844/707281, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 27/29]] (* Harvey P. Dale, Sep 02 2011 *)
Table[29^n*HermiteH[n, 27/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 27/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(54*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(54/29)^(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: A190399 A071803 A215836 * A341561 A079876 A017770

Adjacent sequences: A160286 A160287 A160288 * A160290 A160291 A160292

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved