A160196 Numerator of Hermite(n, 13/28).

1, 13, -223, -13091, 92065, 21723533, 101958529, -49768288739, -926761957183, 144025448042125, 5141947009489249, -497734445201769763, -28642623292540648607, 1968988727426096533261, 171559661755326400233665, -8575534533295174571498723, -1120252760054156502803433599

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..417

Formula

From G. C. Greubel, Sep 25 2018: (Start)

a(n) = 14^n * Hermite(n, 13/28).

E.g.f.: exp(13*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 13/14, -223/196, -13091/2744, 92065/38416, ...

Mathematica

Table[14^n*HermiteH[n, 13/28], {n, 0, 30}] (* G. C. Greubel, Sep 25 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 196*x^2))) \\ G. C. Greubel, Sep 25 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 25 2018

Crossrefs

Cf. A001023 (denominators).

Sequence in context: A068120 A237602 A050523 * A218588 A158518 A223548

Adjacent sequences: A160193 A160194 A160195 * A160197 A160198 A160199

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved