The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A222006 Number of forests of rooted plane binary trees (all nodes have outdegree of 0 or 2) with n total nodes. 3
 1, 1, 1, 2, 2, 4, 5, 10, 12, 27, 35, 79, 104, 244, 331, 789, 1083, 2615, 3652, 8880, 12523, 30657, 43661, 107326, 153985, 379945, 548776, 1357922, 1972153, 4892140, 7139850, 17747863, 26011843, 64776658, 95296413, 237689691, 350844814, 876313458, 1297367201, 3244521203, 4816399289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Here, the binary trees are sized by total number of nodes. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA O.g.f.: Product_{i>=1} 1/(1 - x^i)^A126120(i-1). a(n) ~ c * 2^n / n^(3/2), where c = 1.165663931402962361339366557... if n is even, c = 1.490999501305559555120304528... if n is odd. - Vaclav Kotesovec, Aug 31 2014 EXAMPLE a(6) = 5: There is one forest with 6 trees, one forest with 4 trees and 3 forests with 2 trees, namely 1)...o..o..o..o..o..o............... .................................... 2)...o..o..o....o................... .............../.\.................. ..............o...o................. .................................... 3)...o........o..................... ..../.\....../.\.................... ...o...o....o...o................... .................................... 4).....o....o.....5)......o.....o... ....../.\................/.\........ .....o...o..............o...o....... ..../.\..................../.\...... ...o...o..................o...o..... MAPLE b:= proc(n) option remember; `if`(irem(n, 2)=0, 0, `if`(n<2, n, add(b(i)*b(n-1-i), i=1..n-2))) end: g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(g(n-i*j, i-2)*binomial(b(i)+j-1, j), j=0..n/i))) end: a:= n-> g(n, iquo(n-1, 2)*2+1): seq(a(n), n=0..50); # Alois P. Heinz, Feb 26 2013 MATHEMATICA nn=40; a=Drop[CoefficientList[Series[t=(1-(1-4x^2)^(1/2))/(2x), {x, 0, nn}], x], 1]; CoefficientList[Series[Product[1/(1-x^i)^a[[i]], {i, 1, nn-1}], {x, 0, nn}], x] CROSSREFS Row sums of A342770. Sequence in context: A091188 A147678 A195865 * A127712 A305840 A178113 Adjacent sequences: A222003 A222004 A222005 * A222007 A222008 A222009 KEYWORD nonn AUTHOR Geoffrey Critzer, Feb 23 2013 STATUS approved

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

Last modified June 1 22:32 EDT 2023. Contains 363078 sequences. (Running on oeis4.)