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A160012 revision #9


A160012
Numerator of Hermite(n, 8/25).
1
1, 16, -994, -55904, 2833036, 324848576, -12508897784, -2636506684544, 67268748657296, 27441366823956736, -317711553211272224, -348100470150839555584, -1201073665758439809344, 5202289873610458296810496, 102754085046341979650807936, -89396007427441548519770753024
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Jul 17 2018: (Start)
a(n) = 25^n * Hermite(n, 8/25).
E.g.f.: exp(16*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 16/25, -994/625, -55904/15625, 2833036/390625
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 8/25]] (* Harvey P. Dale, Sep 29 2013 *)
Table[25^n*HermiteH[n, 8/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 8/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(16/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 17 2018
CROSSREFS
Cf. A009969 (denominators).
Sequence in context: A181199 A024301 A211090 * A070307 A159683 A197104
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
editing