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A244531 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 28 05:33 EDT 2020. Contains 337392 sequences. (Running on oeis4.)