A218688 Number of ways to linearly arrange the trees over all forests on n labeled nodes.

1, 1, 3, 15, 106, 975, 11106, 151501, 2415960, 44221869, 915826600, 21211128411, 544126606992, 15334985416075, 471495297242256, 15719617534811625, 565271886957356416, 21820620411482896089, 900398349688515500160, 39564926462522623540519, 1845034125763359894240000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Formula

E.g.f.: 1/(1- T(x) + T(x)^2/2) where T(x) is e.g.f. for A000169.

a(n) = Sum_{m=1..n} A105599(n,m)*m!.

a(n) ~ 4*n^(n-2). - Vaclav Kotesovec, Aug 16 2013

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k^(k-2) * a(n-k). - Ilya Gutkovskiy, Jan 26 2020

Maple

T:= -LambertW(-x):
egf:= 1/(1-T+T^2/2):
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 04 2012

Mathematica

nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[ Series[1/(1-t+t^2/2), {x, 0, nn}], x]

Prog

(PARI) A218688_vec(n, A=List(1))={until(#A>n, listput(A, sum(k=1, #A, binomial(#A, k)*k^(k-2)*A[#A-k+1]))); Vec(A)} \\ M. F. Hasler, Jan 26 2020

Crossrefs

Cf. A101313.

Sequence in context: A128276 A295124 A107878 * A120016 A349874 A074519

Adjacent sequences: A218685 A218686 A218687 * A218689 A218690 A218691

Keyword

nonn

Author

Geoffrey Critzer, Nov 04 2012

Status

approved