|
| |
|
|
A000318
|
|
Generalized tangent numbers d(4,n).
(Formerly M3713 N1517)
|
|
4
|
|
|
|
4, 128, 16384, 4456448, 2080374784, 1483911200768, 1501108249821184, 2044143848640217088, 3605459138582973251584, 7995891855149741436305408, 21776918737280678860353961984, 71454103701490016776039304265728
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 1..100
D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 663-688.
D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699
D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]
|
|
|
FORMULA
|
Equals 2^(4n-2) * A000182(n).
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
|
|
|
MATHEMATICA
|
nn = 30; t = Rest@Union[Range[0, nn - 1]! CoefficientList[Series[Tan[x], {x, 0, nn}], x]]; t2 = t*2^Range[2, 2*nn, 4] (* T. D. Noe, Jun 19 2012 *)
|
|
|
CROSSREFS
|
Cf. A000191.
Sequence in context: A267796 A013823 A130318 * A229385 A141367 A141368
Adjacent sequences: A000315 A000316 A000317 * A000319 A000320 A000321
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000
|
|
|
STATUS
|
approved
|
| |
|
|
