A160059 Numerator of Hermite(n, 13/25).

1, 26, -574, -79924, 74476, 401556376, 9974990776, -2752323059824, -158841568845424, 23393349808258976, 2395194744525753376, -230141809245567612224, -38917614777613866837824, 2440269154465553645576576, 695858238152329730899630976, -24612396011186615794199674624

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, 13/25).

E.g.f.: exp(26*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 26/25, -574/625, -79924/15625, 74476/390625

Maple

seq(coeff(series(factorial(n)*exp(26*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 13/25]] (* Harvey P. Dale, Sep 24 2012 *)
Table[25^n*HermiteH[n, 13/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/25)^(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)*(26/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A265461 A257518 A283343 * A323117 A293612 A197123

Adjacent sequences: A160056 A160057 A160058 * A160060 A160061 A160062

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved