|
|
A000772
|
|
E.g.f. exp(tan(x) + sec(x) - 1).
|
|
5
|
|
|
1, 1, 2, 6, 23, 107, 583, 3633, 25444, 197620, 1684295, 15618141, 156453857, 1683050189, 19344093070, 236497985706, 3063827565763, 41916787157011, 603799270943519, 9132945141812301, 144708157060239704, 2396568154933265024, 41403636316192616995
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The number of elevated increasing binary trees. There is no restriction on the outdegree at the root. - Wenjin Woan, Jan 09 2008
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 2^n * exp(2/Pi - 1 + 4*sqrt(n/Pi) - n) * n^(n - 1/4) / Pi^(n + 1/4). - Vaclav Kotesovec, Jan 27 2020
|
|
MAPLE
|
b:= proc(u, o) option remember;
`if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*b(j, 0), j=1..n))
end:
|
|
MATHEMATICA
|
nn = 25; Range[0, nn]! CoefficientList[Series[Exp[Tan[x] + Sec[x] - 1], {x, 0, nn}], x] (* T. D. Noe, Jun 20 2012 *)
|
|
PROG
|
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(Tan(x) + Sec(x) - 1))); [Factorial(n-1)*b[n]: n in [1..m]]; // Vincenzo Librandi, Jan 30 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|