A160066 Numerator of Hermite(n, 22/25).

1, 44, 686, -79816, -6084404, 131366224, 43807638856, 942289429664, -341856105084784, -24464562920370496, 2769440413707518176, 427662414707761999744, -19262659441336846931264, -7262493236035251261135616, -6531486463827292856927104, 126806246226208496184168487424

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, 22/25).

E.g.f.: exp(44*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 44/25, 686/625, -79816/15625, -6084404/390625, ...

Mathematica

Table[25^n*HermiteH[n, 22/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 22/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/25)^(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: A252869 A296649 A221505 * A358794 A120812 A282860

Adjacent sequences: A160063 A160064 A160065 * A160067 A160068 A160069

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved