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A005801 Generalized tangent numbers of type 3^(2n+1).
(Formerly M5218)
0
0, 30, 217800, 16294301520, 6544151202877440, 9764950519194817858560, 42762698240957239228617722880, 466476501707480855594001261422438400, 11235366943887873286558941529247982529413120 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Ira M. Gessel, 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
Cf. A000182 (tangent numbers).
Sequence in context: A028668 A231815 A291995 * A079601 A307915 A238636
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by Dean Hickerson, Dec 10 2002
More terms from Joe Keane (jgk(AT)jgk.org), Nov 07 2003
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)