|
|
A159705
|
|
Numerator of Hermite(n, 1/21).
|
|
1
|
|
|
1, 2, -878, -5284, 2312620, 23267192, -10152119816, -143434219696, 62392319304592, 1136856492784160, -492996517654282976, -11013067301664857152, 4761026079678523718848, 126084356480177895534464, -54337756316633597169242240, -1665565146450503848398045952
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
D-finite with recurrence a(n) - 2*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 17 2014
a(n) = 21^n * Hermite(n,1/21).
E.g.f.: exp(2*x-441*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/21)^(n-2k)/(k!*(n-2k)!). (End)
|
|
EXAMPLE
|
Numerator of 1, 2/21, -878/441, -5284/9261, 2312620/194481, 23267192/4084101, ...
|
|
MAPLE
|
orthopoly[H](n, 1/21) ;
numer(%) ;
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|