|
|
A143507
|
|
Triangle of coefficients of x^n*H_n(x + 1/x), where H_n(x) is the Hermite polynomial of order n.
|
|
2
|
|
|
1, 2, 0, 2, 4, 0, 6, 0, 4, 8, 0, 12, 0, 12, 0, 8, 16, 0, 16, 0, 12, 0, 16, 0, 16, 32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32, 64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64, 128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128, 256, 0, -1536, 0, -896, 0, 896, 0, 1680, 0, 896, 0, -896, 0, -1536, 0, 256, 512, 0, -4608, 0, 512
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Triangle begins:
1;
2, 0, 2;
4, 0, 6, 0, 4;
8, 0, 12, 0, 12, 0, 8;
16, 0, 16, 0, 12, 0, 16, 0, 16;
32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32;
64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64;
128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128;
|
|
MATHEMATICA
|
Table[CoefficientList[FullSimplify[x^n*HermiteH[n, x + 1/x]], x], {n,
0, 10}]//Flatten
|
|
PROG
|
(PARI) row(n) = Vec(x^n*subst(polhermite(n, x), x, x+1/x));
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|