OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..380
FORMULA
From G. C. Greubel, Jul 17 2018: (Start)
a(n) = 25^n * Hermite(n, 4/25).
E.g.f.: exp(8*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 8/25, -1186/625, -29488/15625, 4211596/390625
MAPLE
seq(coeff(series(factorial(n)*exp(8*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018
MATHEMATICA
Numerator[Table[HermiteH[n, 4/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 4/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 4/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/25)^(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
(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(8/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved