|
|
A170912
|
|
Write cos(x) = Product_{n >= 1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).
|
|
12
|
|
|
-1, 1, 7, 131, 1843, 97261, 4683059, 1331727679, 568285777, 9521655609199, 175554688130609, 11334988388673161, 3457026400678609391, 6594042537777612027841, 249248595232521829462213, 268938575250382935485761673113, 3929672369519648081411955883, 4719016202742955262333630268611
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
EXAMPLE
|
-1/2, 1/24, 7/360, 131/13440, 1843/453600, 97261/47900160, ...
|
|
MAPLE
|
t1:=cos(x);
L:=100;
t0:=series(t1, x, L):
g:=[]; M:=40; t2:=t0:
for n from 1 to M do
t3:=coeff(t2, x, n); t2:=series(t2/(1+t3*x^n), x, L); g:=[op(g), t3];
od:
g;
h:=[seq(g[2*n], n=1..nops(g)/2)];
h1:=map(numer, h);
h2:=map(denom, h);
|
|
MATHEMATICA
|
A[m_, n_] :=
A[m, n] =
Which[m == 1, (-1)^n/(2*n)!, m > n >= 1, 0, True,
A[m - 1, n] - A[m - 1, m - 1]*A[m, n - m + 1]];
a[n_] := Numerator[A[n, n]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|