|
Search: id:A005801
|
|
|
| A005801 |
|
Generalized tangent numbers of type 3^(2n+1).
(Formerly M5218)
|
|
+0
1
|
|
| 0, 30, 217800, 16294301520, 6544151202877440, 9764950519194817858560, 42762698240957239228617722880, 466476501707480855594001261422438400, 11235366943887873286558941529247982529413120
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
|
|
FORMULA
|
a(n) = 1/3^(2*n+1) * sum_{i=0..2*n+1} (-1)^(i+1) * 2^-i * binomial(2*n+1, i) * A000182(n+i+1)
a(n) ~ 2^(1/2)*3^(-1/2)*pi^(-1/2)*n^(-1/2)*2^(8*n)*3^(-3*n)*{1 - 13/144*n^-1 + 169/41472*n^-2 + 48635/17915904*n^-3 - ...} - Joe Keane (jgk(AT)jgk.org), Nov 07 2003
|
|
MATHEMATICA
|
a000182[n_] := (4^n*(4^n-1)*Abs[BernoulliB[2*n]])/(2*n); a[n_] := Sum[((-1)^(i+1)*Binomial[2*n+1, i]*a000182[n+i+1])/2^i, {i, 0, 2*n+1}]/3^(2*n+1)
|
|
CROSSREFS
|
Sequence in context: A115459 A135421 A028668 this_sequence A079601 A159578 A140762
Adjacent sequences: A005798 A005799 A005800 this_sequence A005802 A005803 A005804
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 10 2002
More terms from Joe Keane (jgk(AT)jgk.org), Nov 07 2003
|
|
|
Search completed in 0.002 seconds
|
