A218691 Number of ways to paint some (possibly none or all) of the trees over all forests on n labeled nodes.

1, 2, 6, 26, 156, 1242, 12616, 158034, 2372880, 41725106, 843126624, 19277549898, 492447987136, 13907344659210, 430397513894016, 14487404695687298, 527023721684738304, 20605894357093102434, 861761850029367846400, 38387125875316048363386, 1814541564588778500135936

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: A355206 A242574 A123306 * A099758 A099760 A112934

Adjacent sequences: A218688 A218689 A218690 * A218692 A218693 A218694

Keyword

nonn

Author

Geoffrey Critzer, Nov 04 2012

Status

approved