A159562 Numerator of Hermite(n, 13/18).

1, 13, 7, -4121, -56975, 1929733, 71236279, -949628849, -93127115423, 20066487805, 136040198628199, 1736014871922487, -219855440620458287, -6232933639083272459, 381987420638602610455, 19102129961742695872927, -679901742649149297057599

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, 13/18).

E.g.f.: exp(13*x - 81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 13/18], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[9^n*HermiteH[n, 13/18], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/18)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 81*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/9)^(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: A298085 A177427 A110056 * A249024 A076116 A010216

Adjacent sequences: A159559 A159560 A159561 * A159563 A159564 A159565

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved