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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
OFFSET
0,2
LINKS
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: A363423 A102922 A139688 * A292416 A304985 A292814
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 14 2011
STATUS
approved