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A218691 Number of ways to paint some (possibly none or all) of the trees over all forests on n labeled nodes. 1
1, 2, 6, 26, 156, 1242, 12616, 158034, 2372880, 41725106, 843126624, 19277549898, 492447987136, 13907344659210, 430397513894016, 14487404695687298, 527023721684738304, 20605894357093102434, 861761850029367846400, 38387125875316048363386, 1814541564588778500135936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

a(n) = Sum_{m=1..n} A105599(n,m)*2^m.

a(n) ~ 2*n^(n-2)*exp(1). - Vaclav Kotesovec, Aug 16 2013

MAPLE

T:= -LambertW(-x):

egf:= exp(T-T^2/2)^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[Exp[(t-t^2/2)]^2, {x, 0, nn}], x]

CROSSREFS

Cf. A101313.

Sequence in context: A141761 A242574 A123306 * A099758 A099760 A112934

Adjacent sequences:  A218688 A218689 A218690 * A218692 A218693 A218694

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Nov 04 2012

STATUS

approved

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Last modified April 5 08:42 EDT 2020. Contains 333238 sequences. (Running on oeis4.)