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A160184
Numerator of Hermite(n, 1/28).
1
1, 1, -391, -1175, 458641, 2301041, -896635319, -6308683751, 2454058631585, 22238090874721, -8635680761357159, -95808996990263479, 37141246445981806129, 487826768288181211345, -188783965120435102822039, -2865977269485973590683399, 1107183737638672431002905921
OFFSET
0,3
LINKS
FORMULA
From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 14^n * Hermite(n, 1/28).
E.g.f.: exp(x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 1/14, -391/196, -1175/2744, 458641/38416, ...
MATHEMATICA
Table[14^n*HermiteH[n, 1/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 1/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/14)^(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. A001023 (denominators).
Sequence in context: A318174 A158004 A264448 * A187724 A035883 A235188
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved