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A160067 Numerator of Hermite(n, 23/25). 1
1, 46, 866, -75164, -6705044, 67387976, 45006371896, 1564883287216, -321821122878064, -30452604524550944, 2219667824248876576, 482762276472335122496, -8313367865694637285184, -7623849068906980152558464, -215604829352183231133449344 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Sep 23 2018: (Start)
a(n) = 25^n * Hermite(n, 23/25).
E.g.f.: exp(46*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 46/25, 866/625, -75164/15625, -6705044/390625, ...
MATHEMATICA
Table[25^n*HermiteH[n, 23/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 23/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(46/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018
CROSSREFS
Cf. A009969 (denominators).
Sequence in context: A341428 A066405 A113922 * A156842 A078427 A002138
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified July 13 04:46 EDT 2024. Contains 374267 sequences. (Running on oeis4.)