A159840 Numerator of Hermite(n, 15/22).

1, 15, -17, -7515, -100383, 5768775, 207995055, -5256335475, -431188655295, 3708435650175, 994755425985135, 5946917116353525, -2558835187227126495, -55652375114297534025, 7215309872302076942895, 296779894971771199420125, -21739876411879971311406975

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Formula

E.g.f.: exp(-x*(121*x-15)). - Simon Plouffe, Jun 22 2018

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

a(n) = 11^n * Hermite(n, 15/22).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -15*a(n-1) +242*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021

Mathematica

Numerator[Table[HermiteH[n, 15/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[11^n*HermiteH[n, 15/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 15/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/11)^(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. A159657.

Sequence in context: A157716 A113968 A093812 * A124609 A102500 A067757

Adjacent sequences: A159837 A159838 A159839 * A159841 A159842 A159843

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved