A159510 Numerator of Hermite(n, 9/14).

1, 9, -17, -1917, -12255, 641169, 11775471, -271028133, -10517226303, 117831019545, 10336672775151, -22444344177741, -11344932349212447, -75709842389888607, 13772055231387660015, 227822400841416108939, -18194519582567115241599

Offset

0,2

Links

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

Formula

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

a(n) = 7^n * Hermite(n,9/14).

E.g.f.: exp(9*x-49*x^2).

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

Mathematica

Numerator[Table[HermiteH[n, 9/14], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
With[{nn=20}, CoefficientList[Series[Exp[9x-49x^2], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 11 2021 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/14)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018

Crossrefs

Cf. A159507, A159508, A159509.

Sequence in context: A123836 A141444 A061748 * A191675 A023418 A302232

Adjacent sequences: A159507 A159508 A159509 * A159511 A159512 A159513

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved