A005801 Generalized tangent numbers of type 3^(2n+1). (Formerly M5218)

0, 30, 217800, 16294301520, 6544151202877440, 9764950519194817858560, 42762698240957239228617722880, 466476501707480855594001261422438400, 11235366943887873286558941529247982529413120

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..8.

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

Adjacent sequences: A005798 A005799 A005800 * A005802 A005803 A005804

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Edited by Dean Hickerson, Dec 10 2002

More terms from Joe Keane (jgk(AT)jgk.org), Nov 07 2003

Status

approved