A160221 Numerator of Hermite(n, 23/28).

1, 23, 137, -14881, -503375, 11755783, 1256998009, 1261352591, -3420191427103, -82620004548745, 10166175250198249, 557692448585640127, -31009621361385126767, -3336606569458709073049, 81283079360068297324505, 20180807678470966231356527, -13785930032369364946889279

Offset

0,2

Links

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

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 14^n * Hermite(n, 23/28).

E.g.f.: exp(23*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 23/14, 137/196, -14881/2744, -503375/38416

Mathematica

Table[14^n*HermiteH[n, 23/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Crossrefs

Cf. A001023 (denominators).

Sequence in context: A142679 A254758 A057883 * A042024 A141999 A059915

Adjacent sequences: A160218 A160219 A160220 * A160222 A160223 A160224

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved