|
| |
|
|
A159524
|
|
Numerator of Hermite(n, 7/16).
|
|
1
|
|
|
|
1, 7, -79, -2345, 13921, 1298087, 177169, -995690633, -7128577855, 969687163207, 14999931831409, -1136200046085097, -29073304341219551, 1541690140398172135, 59169809406576537809, -2348520065747488701257, -130045674520859373502079, 3899449373004841245659783
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
|
|
|
FORMULA
|
Conjecture: a(n) -7*a(n-1) +128*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 16^n * Hermite(n,7/16).
E.g.f.: exp(14*x-252*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/8)^(n-2k)/(k!*(n-2k)!). (End)
|
|
|
EXAMPLE
|
Numerator of 1, 7/8, -79/64, -2345/512, 13921/4096, 1298087/32768, 177169/262144,.
|
|
|
MAPLE
|
A159524 := proc(n)
orthopoly[H](n, 7/16) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
|
|
|
MATHEMATICA
|
Numerator[Table[HermiteH[n, 7/16], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
|
|
|
PROG
|
(PARI) a(n)=numerator(polhermite(n, 7/16)) \\ Charles R Greathouse IV, Jan 29 2016
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(7/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
|
|
|
CROSSREFS
|
Cf. A001018 (denominators).
Sequence in context: A235370 A098105 A201301 * A113034 A267798 A201704
Adjacent sequences: A159521 A159522 A159523 * A159525 A159526 A159527
|
|
|
KEYWORD
|
sign,frac
|
|
|
AUTHOR
|
N. J. A. Sloane, Nov 12 2009
|
|
|
STATUS
|
approved
|
| |
|
|
