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A160008 Numerator of Hermite(n, 4/25). 1
1, 8, -1186, -29488, 4211596, 181132768, -24873412856, -1557483062848, 205182497987216, 17216290612377728, -2170572777457158176, -232568214874378865408, 27984829971040893996736, 3712401862884010133093888, -425054272126342446382208896, -68367466777480916900200711168 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Cf. A009969 (denominators).
Sequence in context: A301614 A180767 A240399 * A251699 A162139 A095821
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified April 15 17:59 EDT 2024. Contains 371693 sequences. (Running on oeis4.)