|
Search: id:A000318
|
|
|
| A000318 |
|
Generalized tangent numbers.
(Formerly M3713 N1517)
|
|
+0
1
|
|
| 4, 128, 16384, 4456448, 2080374784, 1483911200768, 1501108249821184, 2044143848640217088, 3605459138582973251584, 7995891855149741436305408, 21776918737280678860353961984, 71454103701490016776039304265728
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699.
|
|
LINKS
|
Thomas Baruchel, Home Page
|
|
FORMULA
|
The g.f. has the following continued fraction expansion: g.f. = [4, b(0), c(0), b(1), c(1), b(2), c(2), ...] where b(n) = sum(k=0, n, 1/(2*k+1))^2 / (128*(n+1)*x), c(n) = -4/( sum(k=0, n, 1/(2*k+1))*sum(k=0, n+1, 1/(2*k+1))*(2*n+3) ), and each convergent of this continued fraction is a Pad'e approximant of the McLaurin series sum(k=1, \infty, a(n)*x^(n-1)). - Thomas Baruchel, Oct 19 2005
|
|
CROSSREFS
|
Equals 2^(4n-2) * A000182(n).
Sequence in context: A128790 A013823 A130318 this_sequence A141367 A141368 A057134
Adjacent sequences: A000315 A000316 A000317 this_sequence A000319 A000320 A000321
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000
|
|
|
Search completed in 0.002 seconds
|
