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

%I A244531 #13 Feb 06 2015 09:14:59
%S A244531 1,0,2,5,11,28,78,201,532,1441,3895,10569,28926,79493,219226,607189,
%T A244531 1687880,4706737,13165215,36929595,103860429,292808814,827392709,
%U A244531 2342964435,6647953886,18898472568,53818654942,153518738980,438602656951,1254943919799,3595714927194
%N A244531 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2.
%H A244531 Alois P. Heinz, <a href="/A244531/b244531.txt">Table of n, a(n) for n = 3..1000</a>
%F A244531 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
%F A244531 a(n) ~ 3^(n+1/2) / (8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jul 02 2014
%p A244531 b:= proc(n, t, k) option remember; `if`(n=0,
%p A244531       `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
%p A244531        b(n-j, max(0, t-1), k), j=1..n)))
%p A244531     end:
%p A244531 a:= n-> b(n-1, 2$2) -b(n-1, 3$2):
%p A244531 seq(a(n), n=3..50);
%t A244531 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 *)
%Y A244531 Column k=2 of A244530.
%Y A244531 Cf. A244456.
%K A244531 nonn
%O A244531 3,3
%A A244531 _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014