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Numerator of Hermite(n, 13/32).
0

%I #22 Feb 06 2021 08:27:17

%S 1,13,-343,-17771,295825,40240733,-234182471,-126663903899,

%T -807320774623,508320180300205,10328296473365449,-2468331468983298763,

%U -90257274834777092687,13992083972581285394941,782649512943833039058905,-90120814247192824203171323

%N Numerator of Hermite(n, 13/32).

%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048">Conjectures of the OEIS database as of June 20, 2018.</a>

%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)

%F Empirical e.g.f.: exp(13*x-256*x^2). - _Simon Plouffe_, Jun 20 2018

%F a(n) = 32^n*KummerU(-n/2, 1/2, (13/32)^2). - _Peter Luschny_, Jun 20 2018

%F D-finite with recurrence a(n) -13*a(n-1) +512*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 06 2021

%e Numerators of 1, 13/16, -343/256, -17771/4096, 295825/65536,...

%p a := n -> 32^n*KummerU(-n/2, 1/2, (13/32)^2):

%p seq(simplify(a(n)), n=0..15); # _Peter Luschny_, Jun 20 2018

%t Numerator[HermiteH[Range[0,20],13/32]] (* _Harvey P. Dale_, Oct 03 2011 *)

%o (PARI) a(n)=numerator(polhermite(n, 13/32)) \\ _Charles R Greathouse IV_, Jan 29 2016

%Y Cf. A001025 (denominators).

%K sign,frac

%O 0,2

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