A244531 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2.

1, 0, 2, 5, 11, 28, 78, 201, 532, 1441, 3895, 10569, 28926, 79493, 219226, 607189, 1687880, 4706737, 13165215, 36929595, 103860429, 292808814, 827392709, 2342964435, 6647953886, 18898472568, 53818654942, 153518738980, 438602656951, 1254943919799, 3595714927194

Offset

3,3

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

Recurrence: (n-2)*n*(n+1)*(31556*n^6 - 602602*n^5 + 4562565*n^4 - 17272550*n^3 + 33523297*n^2 - 29665770*n + 7578864)*a(n) = -2*(n-4)*n*(15778*n^6 - 93541*n^5 - 718683*n^4 + 7746097*n^3 - 25426183*n^2 + 35870760*n - 18623988)*a(n-1) + 2*(189336*n^9 - 4357178*n^8 + 42198478*n^7 - 222932639*n^6 + 692179375*n^5 - 1246825745*n^4 + 1121148607*n^3 - 95771898*n^2 - 622360656*n + 342066240)*a(n-2) + 4*(15778*n^9 - 301301*n^8 + 2556736*n^7 - 13524389*n^6 + 51959635*n^5 - 145042550*n^4 + 255185823*n^3 - 199177680*n^2 - 62590212*n + 146335680)*a(n-3) - 2*(n-4)*(63112*n^8 - 1252538*n^7 + 9554713*n^6 - 31464554*n^5 + 11620330*n^4 + 221568106*n^3 - 627283143*n^2 + 624591414*n - 146644560)*a(n-4) - 4*(n-5)*(n-4)*(504896*n^7 - 9428629*n^6 + 69275668*n^5 - 250040744*n^4 + 437755491*n^3 - 253595994*n^2 - 179277570*n + 187109352)*a(n-5) - 69*(n-6)*(n-5)*(n-4)*(31556*n^6 - 413266*n^5 + 2022895*n^4 - 4417190*n^3 + 3528357*n^2 + 989760*n - 1844640)*a(n-6). - Vaclav Kotesovec, Jul 02 2014

a(n) ~ 3^(n+1/2) / (8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 02 2014

Maple

b:= proc(n, t, k) option remember; `if`(n=0,
      `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
       b(n-j, max(0, t-1), k), j=1..n)))
    end:
a:= n-> b(n-1, 2$2) -b(n-1, 3$2):
seq(a(n), n=3..50);

Mathematica

b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t > n, 0, Sum[b[j - 1, k, k]*b[n - j, Max[0, t - 1], k], {j, 1, n}]]]; T[n_, k_] := b[n - 1, k, k] - If[n == 1 && k == 0, 0, b[n - 1, k + 1, k + 1]]; a[n_] := b[n - 1, 2, 2] - b[n - 1, 3, 3]; Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=2 of A244530.

Cf. A244456.

Sequence in context: A000625 A202476 A210517 * A288390 A127331 A040998

Adjacent sequences: A244528 A244529 A244530 * A244532 A244533 A244534

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved