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A160011
Numerator of Hermite(n, 7/25).
1
1, 14, -1054, -49756, 3255916, 294362824, -16228395464, -2434918716496, 107909598279056, 25859921540866784, -851944079067245024, -335176236367776230336, 7021763778025751855296, 5125948238409003981014144, -42340386055192411914361984, -90296859576930263434548587776
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Jul 17 2018: (Start)
a(n) = 25^n * Hermite(n, 7/25).
E.g.f.: exp(14*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 14/25, -1054/625, -49756/15625, 3255916/390625
MAPLE
seq(coeff(series(factorial(n)*exp(14*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018
MATHEMATICA
Numerator[Table[HermiteH[n, 7/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 7/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 7/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/25)^(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)*(14/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018
CROSSREFS
Cf. A009969 (denominators).
Sequence in context: A208388 A227205 A297766 * A104226 A282272 A208395
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved