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A197356 The number of labeled directed graphs (with self loops allowed) on n nodes of at most two colors, where no edge connects nodes of distinct colors. 2
1, 4, 40, 1216, 140800, 68583424, 138280960000, 1127848949579776, 36911566343372800000, 4836368016228644955357184, 2535397941156689968365568000000, 5316967764024635660932200566930538496, 44601618005626665627415483458173009920000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..35

FORMULA

E.g.f.: A(x)^2 where A(x) is the e.g.f. for A002416.

a(n) = 2^(n^2) * Sum_{k=0..n} C(n,k)*4^(k*(k-n)). - Alois P. Heinz, Oct 14 2011

MAPLE

a:= n-> 2^(n^2) * add(binomial(n, k) * 4^(k*(k-n)), k=0..n):

seq(a(n), n=0..20);  # Alois P. Heinz, Oct 14 2011

MATHEMATICA

a=Sum[2^(n^2)x^n/n!, {n, 0, 20}];  Range[0, 20]!CoefficientList[Series[a^2, {x, 0, 20}], x]

PROG

(PARI) A197356(n)=2^(n^2)*sum(k=0, n, binomial(n, k)*4^(k*(k-n)))  \\ M. F. Hasler, Oct 14 2011

CROSSREFS

Cf. A002416.

Sequence in context: A290000 A102922 A139688 * A292416 A304985 A292814

Adjacent sequences:  A197353 A197354 A197355 * A197357 A197358 A197359

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 14 2011

STATUS

approved

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Last modified May 19 15:03 EDT 2022. Contains 353834 sequences. (Running on oeis4.)