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A158958 Numerator of Hermite(n, 3/4). 1
1, 3, 1, -45, -159, 963, 9249, -18477, -573375, -537597, 39670209, 162018387, -3004923231, -24568534845, 238806411489, 3468095137107, -18252483967359, -498673629451773, 986316931205505, 74767953434671827, 74383686760778721, -11739721489265156157 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
FORMULA
D-finite with recurrence a(n) - 3*a(n-1) + 8*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 10 2018: (Start)
a(n) = 2^n * Hermite(n, 3/4).
E.g.f.: exp(3*x - 4*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/2)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 3/2, 1/4, -45/8, -159/16, 963/32, 9249/64, -18477/128, -573375/256, ...
MAPLE
A158958 := proc(n)
orthopoly[H](n, 3/4) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 3/4], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)
Table[2^n*HermiteH[n, 3/4], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 3/4)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/2)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018
CROSSREFS
Cf. A000079 (denominators).
Sequence in context: A104097 A344379 A155812 * A098341 A354391 A223173
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified February 22 21:30 EST 2024. Contains 370265 sequences. (Running on oeis4.)