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A159530 Numerator of Hermite(n, 2/17). 7

%I #14 Sep 08 2022 08:45:43

%S 1,4,-562,-6872,947020,19676144,-2658183224,-78869600288,

%T 10439530923152,406451155424320,-52680635240539424,

%U -2560010219314727296,324703437982090748608,19055044633095311519488,-2363601454465048638962560,-163647826988867455371547136

%N Numerator of Hermite(n, 2/17).

%H G. C. Greubel, <a href="/A159530/b159530.txt">Table of n, a(n) for n = 0..404</a>

%F From _G. C. Greubel_, Jun 02 2018: (Start)

%F a(n) = 17^n * Hermite(n,2/17).

%F E.g.f.: exp(4*x-289*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/17)^(n-2k)/(k!*(n-2k)!). (End)

%t Numerator[Table[HermiteH[n,2/17],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%o (PARI) /* needs version >= 2.4 */

%o A159530(n)=numerator(polhermite(n,2/17)); /* Joerg Arndt, Apr 30 2011 */

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y The denominators are the powers of 17, A001026.

%Y Cf. A159521, A159529.

%K sign,frac

%O 0,2

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

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)