login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032035 Number of increasing rooted 2,3 cacti (triangular cacti with bridges) with n-1 nodes. 2
1, 1, 1, 3, 13, 77, 573, 5143, 54025, 650121, 8817001, 133049339, 2210979381, 40118485237, 789221836741, 16730904387183, 380227386482641, 9221550336940241, 237724953543108753, 6491255423787076915, 187156557809878784797, 5681772224922980536413 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Also increasing involution rooted trees with n-1 nodes.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

O. Bodini, M. Dien, X. Fontaine, A. Genitrini, H. K. Hwang, Increasing Diamonds, in LATIN 2016: 12th Latin American Symposium, Ensenada, Mexico, April 11-15, 2016, Proceedings Pages pp 207-219 2016, Lecture Notes in Computer Science Series Volume 9644.

C. G. Bower, Transforms (2)

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

FORMULA

E.g.f. of a(n+1) satisfies A'(x) = exp(A(x)+A(x)^2/2).

E.g.f. satisfies A''(x) = 1/(1-A(x)).

Shifts left 2 places under "AIJ" (ordered, indistinct, labeled) transform.

MAPLE

A:= proc(n) option remember; if n=0 then x else convert(series(Int(exp(A(n-1)+ A(n-1)^2/2), x), x=0, n+1), polynom) fi end; a:= n-> if n=1 then 1 else coeff(A(n-1), x, n-1)*(n-1)! fi: seq(a(n), n=1..20); # Alois P. Heinz, Aug 22 2008

MATHEMATICA

CoefficientList[Series[Sqrt[2]*InverseErf[Sqrt[2/(E*Pi)] x + Erf[1/Sqrt[2]]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 07 2014 *)

m = 22; A[_] = 0;

Do[A[x_] = Integrate[Exp[A[x] + A[x]^2/2], x] + O[x]^m, {m}];

CoefficientList[1 + A[x], x]*Range[0, m-1]! (* Jean-Fran├žois Alcover, Sep 29 2019 *)

PROG

(PARI) seq(n)={my(p=x+O(x*x^(n%2))); for(i=1, n\2, p=intformal(1 + intformal(1/(1-p)))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 19 2018

CROSSREFS

Cf. A001147, A091481.

Sequence in context: A189239 A074530 A159662 * A273953 A127127 A043301

Adjacent sequences:  A032032 A032033 A032034 * A032036 A032037 A032038

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Apr 01 1998

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 30 04:54 EDT 2020. Contains 334711 sequences. (Running on oeis4.)