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A160193
Numerator of Hermite(n, 5/28).
2
1, 5, -367, -5755, 402817, 11037925, -734331695, -29632858075, 1866841880705, 102262852326725, -6074903893493615, -431244900588230075, 24038761085803317505, 2148769817796050860325, -111757677404273451703855, -12351237147086094379982875, 595378957401697424118753025
OFFSET
0,2
LINKS
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
FORMULA
D-finite with recurrence a(n) -5*a(n-1) +392*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 09 2018: (Start)
a(n) = 14^n * Hermite(n, 5/28).
E.g.f.: exp(5*x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 5/14, -367/196, -5755/2744, 402817/38416, 11037925/537824,..
MAPLE
A160193 := proc(n)
orthopoly[H](n, 5/28) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
MATHEMATICA
Numerator/@HermiteH[Range[0, 20], 5/28] (* Harvey P. Dale, Jul 11 2011 *)
Table[14^n*HermiteH[n, 5/28], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 5/28)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018
CROSSREFS
Cf. A001023 (denominators).
Sequence in context: A121668 A234311 A237430 * A215437 A098038 A354831
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved