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A160132
Numerator of Hermite(n, 10/27).
1
1, 20, -1058, -79480, 3038092, 524289200, -11661906680, -4819720055200, 22627018472080, 56669755093294400, 836483365475254240, -809515361950727267200, -29605827454506672845120, 13571164223599790810028800, 832572138044715293306980480
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 10/27).
E.g.f.: exp(20*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 20/27, -1058/729, -79480/19683, 3038092/531441, ...
MATHEMATICA
Numerator/@(HermiteH[#, 10/27]&/@Range[0, 20]) (* Harvey P. Dale, Mar 30 2011 *)
Table[27^n*HermiteH[n, 10/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 10/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(20*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
CROSSREFS
Cf. A009971 (denominators).
Sequence in context: A347856 A128482 A128476 * A138915 A006427 A072962
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved