|
| |
|
|
A159658
|
|
Numerator of Hermite(n, 3/20).
|
|
1
|
|
|
|
1, 3, -191, -1773, 109281, 1746243, -104042271, -2407618413, 138436324161, 4267498433283, -236382888189951, -9244145531135853, 492309917424484641, 23662879026999501123, -1209017148222661563231, -69883112720266587834093, 3417402106507184926190721
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
|
|
|
FORMULA
|
D-finite with recurrence a(n) -3*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 10^n * Hermite(n, 3/20).
E.g.f.: exp(3*x - 100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
|
EXAMPLE
|
Numerator of 1, 3/10, -191/100, -1773/1000, 109281/10000, 1746243/100000..
|
|
|
MAPLE
|
A159658 := proc(n)
orthopoly[H](n, 3/20) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
|
|
|
MATHEMATICA
|
Numerator[Table[HermiteH[n, 3/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[10^n*HermiteH[n, 3/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
|
|
|
PROG
|
(PARI) a(n)=numerator(polhermite(n, 3/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/10)^(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. A011557 (denominators).
Sequence in context: A158469 A261000 A032594 * A257038 A202109 A230171
Adjacent sequences: A159655 A159656 A159657 * A159659 A159660 A159661
|
|
|
KEYWORD
|
sign,frac
|
|
|
AUTHOR
|
N. J. A. Sloane, Nov 12 2009
|
|
|
STATUS
|
approved
|
| |
|
|
