A160060 Numerator of Hermite(n, 14/25).

1, 28, -466, -83048, -577844, 399060368, 14785215304, -2578966731488, -201581702391664, 20145379647913408, 2831864782047795424, -172525031701579328128, -43768841640801408267584, 1362347909581250490427648, 749389418131297898080214144, -2858184709995542436237843968

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, 14/25).

E.g.f.: exp(28*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 28/25, -466/625, -83048/15625, -577844/390625...

Maple

seq(coeff(series(factorial(n)*exp(28*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 14/25]] (* Harvey P. Dale, Aug 21 2011 *)
Table[25^n*HermiteH[n, 14/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 14/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/25)^(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)*(28/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A215767 A079518 A320820 * A115226 A086782 A115225

Adjacent sequences: A160057 A160058 A160059 * A160061 A160062 A160063

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved