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A160197
Numerator of Hermite(n, 15/28).
1
1, 15, -167, -14265, -17583, 22103775, 366019305, -46497789225, -1701823811295, 120289709840175, 7808380053851385, -354409961765715225, -38985884218692900495, 1082356196865530910975, 214907408931441984587145, -2716359674426403870623625
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Sep 25 2018: (Start)
a(n) = 14^n * Hermite(n, 15/28).
E.g.f.: exp(15*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 15/14, -167/196, -14265/2744, -17583/38416, ...
MATHEMATICA
Table[14^n*HermiteH[n, 15/28], {n, 0, 30}] (* G. C. Greubel, Sep 25 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 15/28)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(15*x - 196*x^2))) \\ G. C. Greubel, Sep 25 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 25 2018
CROSSREFS
Cf. A001023 (denominators).
Sequence in context: A167615 A210326 A016234 * A055660 A121114 A121116
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved