A159832 Numerator of Hermite(n, 13/22).

1, 13, -73, -7241, -41135, 6474533, 133942279, -7659772289, -326475260383, 10585140766525, 848669947078999, -14583331342963513, -2448742706582821007, 10516339034389368661, 7840456962356616680615, 66296583862124835824527, -27599003183146895684913599

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, 13/22).

E.g.f.: exp(13*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 13/11, -73/121, -7241/1331, -41135/14641, ...

Mathematica

Numerator/@Table[HermiteH[n, 13/22], {n, 0, 20}]  (* Harvey P. Dale, Apr 16 2011 *)
Table[11^n*HermiteH[n, 13/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A220414 A139157 A228027 * A139070 A094421 A301882

Adjacent sequences: A159829 A159830 A159831 * A159833 A159834 A159835

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved