|
|
A159784
|
|
Numerator of Hermite(n, 19/21).
|
|
1
|
|
|
1, 38, 562, -45676, -3222740, 38680808, 15682154104, 391223020016, -81955144677488, -5874765126977440, 427318863624757024, 68053545237681787712, -1559812895855484713792, -779551612838132460267904, -11738146623970045761841280, 9179853743614397880438109952
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 21^n * Hermite(n, 19/21).
E.g.f.: exp(38*x - 441*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/21)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
MATHEMATICA
|
Table[21^n*HermiteH[n, 19/21], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
|
|
PROG
|
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/21)^(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
|
|
|
|