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A007748 Number of self-converse oriented trees with n nodes. 1

%I

%S 1,1,1,2,3,7,10,26,39,107,160,458,702,2058,3177,9498,14830,44947,

%T 70678,216598,342860,1059952,1686486,5251806,8393681,26297238,

%U 42187148,132856766,213828802,676398395,1091711076

%N Number of self-converse oriented trees with n nodes.

%H R. Simion, <a href="http://dx.doi.org/10.1016/0012-365X(91)90061-6">Trees with 1-factors and oriented trees</a>, Discrete Math., 88 (1991), 93-104.

%H R. Simion, <a href="/A005750/a005750.pdf">Trees with 1-factors and oriented trees</a>, Discrete Math., 88 (1981), 97. (Annotated scanned copy)

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(2n)=A000151(n). a(2n-1)=A005750(n). - _Christian G. Bower_, Dec 15 1999.

%t max = 15; A[n_, k_] := A[n, k] = If[n<2, n, Sum[Sum[d*A[d, k], {d, Divisors[j]}] * A[n-j, k]*k, {j, 1, n-1}]/(n-1)]; a[n_] := A[n, 2]; A000151 = Table[a[n], {n, 1, max}]; etr[p_] := Module[{b}, b[n_] := b[n] = If[n==0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; A005750 = Table[etr[a][n], {n, 0, max}] ; A007748 = Riffle[A005750, A000151] (* _Jean-Fran├žois Alcover_, Jul 16 2015 *)

%Y Cf. A000238.

%K nonn,nice

%O 1,4

%A _N. J. A. Sloane_.

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Last modified April 14 16:51 EDT 2021. Contains 342950 sequences. (Running on oeis4.)