A160064 Numerator of Hermite(n, 19/25).

1, 38, 194, -87628, -4057364, 283960168, 36149011384, -756038827408, -345033325051504, -5550878077877152, 3670691539870088224, 208872254488527752512, -42534863002649658484544, -4749408611428603310092672, 510713996558770024590318464, 102521782569233818861053861632

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, 19/25).

E.g.f.: exp(38*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 38/25, 194/625, -87628/15625, -4057364/390625, ...

Mathematica

Table[25^n*HermiteH[n, 19/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/25)^(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: A100167 A100168 A137022 * A297541 A235079 A005910

Adjacent sequences: A160061 A160062 A160063 * A160065 A160066 A160067

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved