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A160270
Numerator of Hermite(n, 16/29).
1
1, 32, -658, -128704, -798260, 840376192, 33605404744, -7405703577856, -632652549947248, 79406265745318400, 12118094804951629024, -947834356077803359232, -254539689475704747697472, 10985818579851831076419584, 5917311044631018607598349440
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 29^n * Hermite(n, 16/29).
E.g.f.: exp(32*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 32/29, -658/841, -128704/24389, -798260/707281, ...
MATHEMATICA
Numerator/@HermiteH[Range[0, 20], 16/29] (* Harvey P. Dale, Jun 07 2011 *)
Table[29^n*HermiteH[n, 16/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 16/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/29)^(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: A028152 A028176 A028151 * A028102 A028143 A028101
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved