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A058876 Triangle read by rows: T(n,k) = number of labeled acyclic digraphs with n nodes, containing exactly n+1-k points of in-degree zero (n >= 1, 1<=k<=n). 5
1, 1, 2, 1, 9, 15, 1, 28, 198, 316, 1, 75, 1610, 10710, 16885, 1, 186, 10575, 211820, 1384335, 2174586, 1, 441, 61845, 3268125, 64144675, 416990763, 654313415, 1, 1016, 336924, 43832264, 2266772550, 44218682312, 286992935964, 450179768312 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 19, (1.6.4).

R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.

LINKS

Table of n, a(n) for n=1..36.

R. W. Robinson, Enumeration of acyclic digraphs, Manuscript. (Annotated scanned copy)

FORMULA

Harary and Prins (following Robinson) give a recurrence.

EXAMPLE

Triangle begins:

1;

1,  2;

1,  9,  15;

1, 28, 198, 316;

...

MATHEMATICA

a[p_, k_] :=a[p, k] =If[p == k, 1, Sum[Binomial[p, k]*a[p - k, n]*(2^k - 1)^n*2^(k (p - k - n)), {n, 1, p - k}]];

Map[Reverse, Table[Table[a[p, k], {k, 1, p}], {p, 1, 6}]] // Grid (* Geoffrey Critzer, Aug 29 2016 *)

CROSSREFS

Columns give A058877, A003025, A003026. Row sums give A003024.

Sequence in context: A180001 A204371 A199887 * A214884 A083162 A178075

Adjacent sequences:  A058873 A058874 A058875 * A058877 A058878 A058879

KEYWORD

nonn,easy,tabl

AUTHOR

N. J. A. Sloane, Jan 07 2001

EXTENSIONS

More terms from Vladeta Jovovic, Apr 10 2001

STATUS

approved

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Last modified November 20 15:12 EST 2018. Contains 317402 sequences. (Running on oeis4.)