A160070 Numerator of Hermite(n, 3/26).

1, 3, -329, -3015, 324561, 5049963, -533358201, -11841399567, 1226401304865, 35698348343763, -3623617724368041, -131531270575023063, 13078016887475307249, 572724884114719465275, -55746631551222341656281, -2877374046284519534650143, 274003299825843713593394241

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..423

Formula

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

a(n) = 13^n * Hermite(n, 3/26).

E.g.f.: exp(3*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 3/13, -329/169, -3015/2197, 324561/28561, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 3/26]] (* Harvey P. Dale, Jun 11 2018 *)
Table[13^n*HermiteH[n, 3/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/13)^(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. A001022 (denominators).

Sequence in context: A272318 A320284 A235334 * A112895 A157585 A045645

Adjacent sequences: A160067 A160068 A160069 * A160071 A160072 A160073

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved