A160075 Numerator of Hermite(n, 15/26).

1, 15, -113, -11835, -62943, 15056775, 332225295, -25551760275, -1169321452095, 51552138002175, 4330357927305615, -109290857537767275, -17739633636788785695, 177189213621352281975, 80605788404370208573455, 370627467209314130296125, -403111935202017245512974975

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, 15/26).

E.g.f.: exp(15*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 15/13, -113/169, -11835/2197, -62943/28561

Mathematica

Numerator[HermiteH[Range[0, 20], 15/26]] (* Harvey P. Dale, Mar 13 2018 *)
Table[13^n*HermiteH[n, 15/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 15/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(15*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/13)^(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: A115138 A233326 A092317 * A244872 A293875 A044347

Adjacent sequences: A160072 A160073 A160074 * A160076 A160077 A160078

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved