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A218688 Number of ways to linearly arrange the trees over all forests on n labeled nodes. 3
1, 1, 3, 15, 106, 975, 11106, 151501, 2415960, 44221869, 915826600, 21211128411, 544126606992, 15334985416075, 471495297242256, 15719617534811625, 565271886957356416, 21820620411482896089, 900398349688515500160, 39564926462522623540519, 1845034125763359894240000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 15:20 EST 2022. Contains 350657 sequences. (Running on oeis4.)