login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A290355 The sixth Euler transform of the sequence with g.f. 1+x. 3
1, 1, 6, 21, 91, 336, 1337, 5026, 19193, 71769, 268272, 992676, 3659116, 13400426, 48863017, 177299790, 640713627, 2305930966, 8268556438, 29544196129, 105215495691, 373523546056, 1322096328899, 4666327388034, 16425341129078, 57667752483279, 201967215942032 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of 6-level rooted trees with n leaves. All n leaves are in level 6. a(2) = 6:

:    o      o      o      o      o      o

:    |      |      |      |      |     ( )

:    o      o      o      o      o     o o

:    |      |      |      |     ( )    | |

:    o      o      o      o     o o    o o

:    |      |      |     ( )    | |    | |

:    o      o      o     o o    o o    o o

:    |      |     ( )    | |    | |    | |

:    o      o     o o    o o    o o    o o

:    |     ( )    | |    | |    | |    | |

:    o     o o    o o    o o    o o    o o

:   ( )    | |    | |    | |    | |    | |

:   o o    o o    o o    o o    o o    o o

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.

Index entries for sequences related to rooted trees

FORMULA

G.f.: Product_{j>0} 1/(1-x^j)^A007714(j).

MAPLE

with(numtheory):

b:= proc(n, k) option remember; `if`(n<2, 1, `if`(k=0, 0, add(

      add(b(d, k-1)*d, d=divisors(j))*b(n-j, k), j=1..n)/n))

    end:

a:= n-> b(n, 6):

seq(a(n), n=0..30);

MATHEMATICA

b[n_, k_]:=b[n, k]=If[n<2, 1, If[k==0, 0, Sum[Sum[b[d, k - 1]*d, {d, Divisors[j]}] b[n - j, k], {j, n}]/n]]; Table[b[n, 6], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *)

CROSSREFS

Column k=6 of A290353.

Cf. A007714.

Sequence in context: A304187 A005498 A002222 * A006359 A001553 A009247

Adjacent sequences:  A290352 A290353 A290354 * A290356 A290357 A290358

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 28 2017

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 December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)