A160069 Numerator of Hermite(n, 1/26).

1, 1, -337, -1013, 340705, 1710281, -574081169, -4042531037, 1354233514817, 12285237438865, -4107293114634449, -45631395657998149, 15225284404552883233, 200306225193393375577, -66699593448411975550225, -1014548651063549428780589, 337152390132385166610860161

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..422

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 13^n * Hermite(n, 1/26).

E.g.f.: exp(x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 1/13, -337/169, -1013/2197, 340705/28561, ...

Mathematica

Table[13^n*HermiteH[n, 1/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A001022 (denominators).

Sequence in context: A157999 A152853 A142830 * A201852 A251271 A263865

Adjacent sequences: A160066 A160067 A160068 * A160070 A160071 A160072

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved