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 A160194 Numerator of Hermite(n, 9/28). 1

%I

%S 1,9,-311,-9855,277041,17946009,-381486279,-45642389679,636016842465,

%T 148858685615529,-904139249676759,-591663300859964511,

%U -1426321263133495791,2770347275877071597625,32201658639821938929561,-14913850922254971477399951,-323570411102447744202418239

%N Numerator of Hermite(n, 9/28).

%H G. C. Greubel, <a href="/A160194/b160194.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Jul 12 2018: (Start)

%F a(n) = 14^n * Hermite(n, 9/28).

%F E.g.f.: exp(9*x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 9/14, -311/196, -9855/2744, 277041/38416, ...

%t Numerator[Table[HermiteH[n, 9/28], {n, 0, 30}]] (* or *) Table[14^n* HermiteH[n, 9/28], {n,0,30}] (* _G. C. Greubel_, Jul 12 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 9/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(9/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 12 2018

%Y Cf. A001023 (denominators).

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009

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Last modified January 29 04:46 EST 2020. Contains 331335 sequences. (Running on oeis4.)