|
| |
|
|
A006229
|
|
Expansion of exp( tan x ).
(Formerly M2822)
|
|
7
| |
|
|
1, 1, 1, 3, 9, 37, 177, 959, 6097, 41641, 325249, 2693691, 24807321, 241586893, 2558036145, 28607094455, 342232522657, 4315903789009, 57569080467073, 807258131578995, 11879658510739497, 183184249105857781
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259, Sum_{k} T(n,k).
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
L. B. W. Jolley, Summation of Series. 2nd ed., Dover, NY, 1961, p. 150.
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=0..100
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
|
|
|
FORMULA
| E.g.f.: exp(tan(x)).
a(n)=sum(if oddp(n+k) then 0 else (-1)^((n+k)/2)*sum(j!/k!*stirling2(n,j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1,k-1),j,k,n),k,1,n), n>0 [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 05 2010]
|
|
|
MAPLE
| a(n):=sum(if oddp(n+k) then 0 else (-1)^((n+k)/2)*sum(j!/k!*stirling2(n, j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1, k-1), j, k, n), k, 1, n); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 05 2010]
|
|
|
MATHEMATICA
| With[{nn=30}, CoefficientList[Series[Exp[Tan[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* From Harvey P. Dale, Oct 04 2011 *)
|
|
|
CROSSREFS
| Cf. A003711, A003717.
Cf. A047691, A047692. Row sums of A059419 and unsigned A111593.
Sequence in context: A002751 A119856 A077365 * A008986 A105215 A158053
Adjacent sequences: A006226 A006227 A006228 * A006230 A006231 A006232
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
|
|
|
EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001
|
| |
|
|
