A007152 Evolutionary trees of magnitude n. (Formerly M3628)

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

Offset

1,3

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

Table of n, a(n) for n=1..20.

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

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 *)

Crossrefs

Cf. A007151.

Sequence in context: A354147 A362475 A274043 * A345248 A295258 A177554

Adjacent sequences: A007149 A007150 A007151 * A007153 A007154 A007155

Keyword

nonn,easy

Author

Robert W. Robinson

Status

approved