A160396 Numerator of Hermite(n, 13/32).

1, 13, -343, -17771, 295825, 40240733, -234182471, -126663903899, -807320774623, 508320180300205, 10328296473365449, -2468331468983298763, -90257274834777092687, 13992083972581285394941, 782649512943833039058905, -90120814247192824203171323

Offset

0,2

Links

Table of n, a(n) for n=0..15.

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

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

Formula

Empirical e.g.f.: exp(13*x-256*x^2). - Simon Plouffe, Jun 20 2018

a(n) = 32^n*KummerU(-n/2, 1/2, (13/32)^2). - Peter Luschny, Jun 20 2018

D-finite with recurrence a(n) -13*a(n-1) +512*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021

Example

Numerators of 1, 13/16, -343/256, -17771/4096, 295825/65536,...

Maple

a := n -> 32^n*KummerU(-n/2, 1/2, (13/32)^2):
seq(simplify(a(n)), n=0..15); # Peter Luschny, Jun 20 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 13/32]] (* Harvey P. Dale, Oct 03 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/32)) \\ Charles R Greathouse IV, Jan 29 2016

Crossrefs

Cf. A001025 (denominators).

Sequence in context: A096717 A296679 A125119 * A253125 A297070 A220636

Adjacent sequences: A160393 A160394 A160395 * A160397 A160398 A160399

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved