A160071 Numerator of Hermite(n, 5/26).

1, 5, -313, -4945, 292657, 8148925, -453845705, -18795248425, 979822695905, 55721465220725, -2702013314839385, -201848619020247425, 9036842409471596305, 863882210793481537325, -35388474493250786477545, -4264832993941008567009625, 158095400711076444606105025

Offset

0,2

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, 5/26).

E.g.f.: exp(5*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 5/13, -313/169, -4945/2197, 292657/28561, ...

Mathematica

Table[13^n*HermiteH[n, 5/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/13)^(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: A300610 A301352 A075983 * A094161 A366305 A130308

Adjacent sequences: A160068 A160069 A160070 * A160072 A160073 A160074

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved