A159552 Numerator of Hermite(n, 7/18).

1, 7, -113, -3059, 33505, 2216767, -11621681, -2236049291, -2473358783, 2880606369655, 23770401693199, -4500189506988707, -73860182366201567, 8231347125022635439, 213168973938378948175, -17176512461982684538427, -638236193904139635834239

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 9^n * Hermite(n, 7/18).

E.g.f.: exp(7*x - 81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 7/18], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[9^n*HermiteH[n, 7/18], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/18)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 81*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A159545, A159546.

Sequence in context: A152927 A064330 A371328 * A228929 A086788 A199672

Adjacent sequences: A159549 A159550 A159551 * A159553 A159554 A159555

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved