A160065 Numerator of Hermite(n, 21/25).

1, 42, 514, -83412, -5430804, 188966232, 41879106744, 341675743248, -352091802793584, -18204613149810528, 3196439029135777824, 361808103596334268608, -28755096299570905798464, -6634835598526992072655488, 188607219729893552173509504, 124031126202877890462758439168

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..380

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 21/25).

E.g.f.: exp(42*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 42/25, 514/625, -83412/15625, -5430804/390625, ...

Mathematica

Table[25^n*HermiteH[n, 21/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 21/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(42/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A263289 A273223 A163727 * A196671 A248448 A248449

Adjacent sequences: A160062 A160063 A160064 * A160066 A160067 A160068

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved