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A158954 Numerator of Hermite(n, 1/4). 7
1, 1, -7, -23, 145, 881, -4919, -47207, 228257, 3249505, -13184999, -273145399, 887134513, 27109092817, -65152896535, -3101371292039, 4716976292161, 401692501673153, -239816274060743, -58083536514994775, -21631462857761839, 9271734379541402161 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
FORMULA
D-finite with recurrence a(n) - a(n-1) + 8*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 2^n*Hermite(n,1/4).
E.g.f.: exp(x-4*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/2)^(n-2k)/(k!*(n-2k)!)). (End)
EXAMPLE
Numerators of 1, 1/2, -7/4, -23/8, 145/16, 881/32, -4919/64, -47207/128, 228257/256, 3249505/512, ...
MAPLE
A158954 := proc(n)
orthopoly[H](n, 1/4) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 1/4], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 1/4)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/2)^(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
CROSSREFS
Cf. A000079 (denominators).
Sequence in context: A082021 A227254 A080082 * A056205 A099051 A187487
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)