A159808 Numerator of Hermite(n, 5/22).

1, 5, -217, -3505, 140017, 4092925, -148955945, -6687706825, 218892836705, 14041864596725, -406539275359865, -36014008700873825, 902137507503591505, 109095368804855545325, -2292647754582021148105, -381078348283760693301625, 6416919607713933301113025

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

Formula

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 11^n * Hermite(n, 5/22).

E.g.f.: exp(5*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 5/11, -217/121, -3505/1331, 140017/14641, ...

Mathematica

Numerator[Table[HermiteH[n, 5/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[11^n*HermiteH[n, 5/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A291806 A119657 A235456 * A159317 A345465 A346196

Adjacent sequences: A159805 A159806 A159807 * A159809 A159810 A159811

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved