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A160285 Numerator of Hermite(n, 23/29). 1
1, 46, 434, -134780, -8389844, 520867016, 94518470776, -908740269776, -1154662527326320, -40886467186904864, 15598503848068208416, 1405241555094877399616, -223962406662593631730496, -38665666254514312493452160, 3118541336376613976720226176 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 23/29).
E.g.f.: exp(46*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 46/29, 434/841, -134780/24389, -8389844/707281, ...
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 23/29]] (* Harvey P. Dale, Sep 28 2015 *)
Table[29^n*HermiteH[n, 23/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 23/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(46/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
CROSSREFS
Cf. A009973 (denominators).
Sequence in context: A272184 A213286 A135735 * A111304 A055751 A232071
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified April 17 08:54 EDT 2024. Contains 371763 sequences. (Running on oeis4.)