A006706 Self-convolution of numbers of trees on n nodes.

1, 2, 3, 4, 7, 12, 23, 44, 90, 186, 407, 902, 2072, 4844, 11595, 28150, 69491, 173522, 438423, 1117968, 2875960, 7453070, 19447591, 51050224, 134749849, 357446716, 952527403, 2548897192, 6846986075, 18458150242, 49923931099, 135443922536, 368511905808

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to trees

Formula

a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856519949747148175..., c = 1.67518821170655279423478... . - Vaclav Kotesovec, Aug 25 2014

Maple

with(numtheory): b:= proc(n) option remember; local d, j; if n<=1 then n else (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/ (n-1) fi end: t:= proc(n) option remember; local k; `if`(n=0, 1, b(n)- (add(b(k) *b(n-k), k=1..n-1) -`if`(type(n, odd), 0, b(n/2)))/2) end: a:= n-> add(t(j)* t(n-j), j=0..n): seq(a(n), n=0..40);  # Alois P. Heinz, Oct 28 2008

Mathematica

b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}])/(n-1)]; t[n_] := t[n] = If[n == 0, 1, b[n] - (Sum [b[k]*b[n-k], {k, 1, n-1}] - If[OddQ[n], 0, b[n/2]])/2]; a[n_] := Sum[t[j]*t[n-j], {j, 0, n}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 28 2014, after Alois P. Heinz *)

Crossrefs

Cf. A000055.

Sequence in context: A141002 A006537 A103963 * A194079 A124390 A215981

Adjacent sequences: A006703 A006704 A006705 * A006707 A006708 A006709

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Alois P. Heinz, Oct 28 2008

Status

approved