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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 (list; graph; refs; listen; history; text; internal format)
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, 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

Adjacent sequences:  A160008 A160009 A160010 * A160012 A160013 A160014

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)