A007152 Evolutionary trees of magnitude n.

1, 1, 4, 28, 301, 4466, 84974, 1974904, 54233540, 1718280152, 61695193880, 2475688513024, 109797950475448, 5333253012414224, 281576039542538368, 16055279332196218624, 983264280857581866112, 64369946360185677026048, 4485859513184032011682304, 331558482325457407154881024

Offset: 1

Author

Robert W. Robinson

Keywords

• nonn
• easy

References

• L. R. Foulds and R. W. Robinson, Counting certain classes of evolutionary trees with singleton labels, Congress. Num., 44 (1984), 65-88.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• L. R. Foulds and R. W. Robinson, Counting certain classes of evolutionary trees with singleton labels, Congress. Num., 44 (1984), 65-88. (Annotated scanned copy)
• Index entries for sequences related to trees

Crossrefs

Cf. A007151.

Programs

Maple

Q  := proc(n)
    option remember ;
    if n <= 1 then
        0;
    else
        A007151(n)-A007151(n-1) +(n-1)*procname(n-1) ; # eq (3.5)
        %/2 ;
    end if;
end proc:
A007152 := proc(n)
    if n = 1 then
        1;
    else
        A007151(n-1)+Q(n-1) ; # eq (3.9)
    end if ;
end proc:
seq(A007152(n),n=1..20 ); # R. J. Mathar, Mar 19 2018

Mathematica

m = 20;
A007151 = Rest[Range[0, m]! CoefficientList[ InverseSeries[ Series[(2x - E^x + 1)/(x + 1), {x, 0, m}], x], x]];
Q[n_] := Q[n] = If[n <= 1, 0, (1/2)(-A007151[[n - 1]] + A007151[[n]] + (n - 1) Q[n - 1])];
a[n_] := If[n == 1, 1, A007151[[n - 1]] + Q[n - 1]];
Array[a, m] (* Jean-François Alcover, Mar 30 2020, from Maple *)