A160062 Numerator of Hermite(n, 17/25).

1, 34, -94, -88196, -2646164, 351010424, 28472879416, -1664500279856, -305730704405104, 6250158848786464, 3651975825416159776, 46040192454318632384, -48649301056025363418944, -2344679122719641842004096, 710832051987944332929700736, 65200174415183839554681505024

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, 17/25).

E.g.f.: exp(34*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 34/25, -94/625, -88196/15625, -2646164/390625, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 17/25]] (* Harvey P. Dale, Feb 04 2015 *)
Table[25^n*HermiteH[n, 17/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 17/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/25)^(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: A202421 A365248 A202414 * A247218 A233031 A233028

Adjacent sequences: A160059 A160060 A160061 * A160063 A160064 A160065

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved