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A160075 Numerator of Hermite(n, 15/26). 1
1, 15, -113, -11835, -62943, 15056775, 332225295, -25551760275, -1169321452095, 51552138002175, 4330357927305615, -109290857537767275, -17739633636788785695, 177189213621352281975, 80605788404370208573455, 370627467209314130296125, -403111935202017245512974975 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)