|
|
A321394
|
|
a(n) = (1/24)*n!*[x^n] (9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x)) where sectan(x) = sec(x) + tan(x).
|
|
3
|
|
|
1, 1, 2, 10, 75, 816, 11407, 194480, 3871075, 87700736, 2220246387, 62010892800, 1892138207375, 62591994720256, 2230631475837767, 85188256574494720, 3470563987113896475, 150234341045137637376, 6886077311552162511547, 333165973379285030666240, 16967906593223743786978375
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
See A320956 for motivation and definitions.
|
|
LINKS
|
|
|
MAPLE
|
sectan := x -> sec(x) + tan(x): # sin(Pi/4 + x/2)*csc(Pi/4 - x/2)
egf := 9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x):
ser := series(egf, x, 22): seq((1/24)*n!*coeff(ser, x, n), n=0..20);
|
|
MATHEMATICA
|
m = 20;
sectan[x_] := Sec[x] + Tan[x];
egf = 9 + sectan[4x] + 6 sectan[2x] + 8 sectan[x];
|
|
PROG
|
(PARI) sectan(x) = 1/cos(x) + tan(x);
my(x='x+O('x^25)); Vec(serlaplace(9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x)))/24 \\ Michel Marcus, Aug 19 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|