|
|
A158965
|
|
Numerator of Hermite(n, 3/5).
|
|
1
|
|
|
1, 6, -14, -684, -2004, 124776, 1249656, -29934864, -616988784, 8272012896, 327277030176, -2172344266944, -193036432198464, 145187966975616, 126344808730855296, 656437275502200576, -90819982895128268544, -1070069717772530072064, 70776567154223847830016
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 5^n * Hermite(n, 3/5).
E.g.f.: exp(6*x - 25*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
MATHEMATICA
|
Table[5^n*HermiteH[n, 3/5], {n, 0, 30}] (* G. C. Greubel, Jul 13 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 25*x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|