A005755 Number of identity matched trees with n nodes. (Formerly M3517)

0, 0, 0, 1, 4, 16, 64, 252, 1018, 4182, 17510, 74510, 322034, 1410362, 6251114, 27998532, 126583634, 577079333, 2650573354, 12256481666, 57021299394, 266754944481, 1254245360430, 5924659521632, 28105641930102, 133853504339029, 639801068848128

Offset

1,5

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..450

Rodica Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104.

Rodica Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1981), 97. (Annotated scanned copy)

Index entries for sequences related to trees

Formula

a(n) ~ c * d^n / n^(5/2), where d = A246312 = 5.2490324912281705791649522..., c = 0.089035519570392123219315... . - Vaclav Kotesovec, Aug 25 2014

Maple

with(numtheory): b2:= proc(n) option remember; local m; `if`(n=1, 1, 2/(n-1) *add(b2(m) *add((-1)^((n-m)/d+1) *d*b2(d), d=divisors(n-m)), m=1..n-1)) end: c2:= proc(n) option remember; local m; `if`(n=1, 1, 1/(n-1) *add(c2(m) *add((-1)^((n-m)/d+1) *d*b2(d), d=divisors(n-m)), m=1..n-1)) end: a2:= n-> (b2(n) -add(b2(m) *b2(n-m), m=1..n-1) -`if`(irem(n, 2)=0, b2(n/2), c2((n+1)/2)))/2: seq(a2(n), n=1..30); # Alois P. Heinz, Aug 04 2009

Mathematica

b2[n_] := b2[n] = If [n == 1, 1, 2/(n-1)*Sum[b2[m]*Sum[(-1)^((n-m)/d+1)*d*b2[d], {d, Divisors[n-m]}], {m, 1, n-1}]]; c2[n_] := c2[n] = If [n == 1, 1, 1/(n-1)*Sum[c2[m]*Sum[(-1)^((n-m)/d+1)*d*b2[d], {d, Divisors[n-m]}], {m, 1, n-1}]]; a2[n_] := (b2[n] - Sum[b2[m]*b2[n-m], {m, 1, n-1}] - If[Mod[n, 2] == 0, b2[n/2], c2[(n+1)/2]])/2; Table[a2[n], {n, 1, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)

Crossrefs

Cf. A005753, A005754, A102755, A246312.

Sequence in context: A269771 A228980 A188714 * A269651 A077821 A215877

Adjacent sequences: A005752 A005753 A005754 * A005756 A005757 A005758

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Aug 04 2009

Status

approved