A160013 Numerator of Hermite(n, 9/25).

1, 18, -926, -61668, 2362476, 350864568, -8449912776, -2783582689968, 23832248370576, 28264807370350368, 240653738497326624, -348978324836427720768, -9590598751393940053824, 5062044095021324890551168, 246964023420535373904561024, -84140419241303548854363341568

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, 9/25).

E.g.f.: exp(18*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 18/25, -926/625, -61668/15625, 2362476/390625

Maple

seq(coeff(series(factorial(n)*exp(18*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 9/25]] (* Harvey P. Dale, Oct 10 2012 *)
Table[25^n*HermiteH[n, 9/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/25)^(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)*(18/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A201538 A214160 A242446 * A356687 A123786 A333089

Adjacent sequences: A160010 A160011 A160012 * A160014 A160015 A160016

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved