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A219034 Triangular array read by rows: T(n,k) is the number of forests of rooted trees on n labeled nodes with exactly k isolated nodes; n>=0, 0<=k<=n. 1
1, 0, 1, 2, 0, 1, 9, 6, 0, 1, 76, 36, 12, 0, 1, 805, 380, 90, 20, 0, 1, 10626, 4830, 1140, 180, 30, 0, 1, 167839, 74382, 16905, 2660, 315, 42, 0, 1, 3091768, 1342712, 297528, 45080, 5320, 504, 56, 0, 1, 65127465, 27825912, 6042204, 892584, 101430, 9576, 756, 72, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column k=0 is A105785.

Row sums = (n+1)^(n-1).

LINKS

Table of n, a(n) for n=0..54.

FORMULA

E.g.f.: exp(T(x)-x+y*x) where T(x) is the e.g.f. for A000169.

EXAMPLE

1;

0, 1;

2, 0, 1;

9, 6, 0, 1;

76, 36, 12, 0, 1;

805, 380, 90, 20, 0, 1;

10626, 4830, 1140, 180, 30, 0, 1;

167839, 74382, 16905, 2660, 315, 42, 0, 1;

3091768, 1342712, 297528, 45080, 5320, 504, 56, 0, 1;

MATHEMATICA

nn=8; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[ Series[Exp[t-x+y x], {x, 0, nn}], {x, y}] //Grid

CROSSREFS

Sequence in context: A255306 A072551 A256117 * A256116 A185410 A264676

Adjacent sequences:  A219031 A219032 A219033 * A219035 A219036 A219037

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Nov 10 2012

STATUS

approved

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Last modified April 4 04:53 EDT 2020. Contains 333212 sequences. (Running on oeis4.)