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.

1, 4, 40, 1216, 140800, 68583424, 138280960000, 1127848949579776, 36911566343372800000, 4836368016228644955357184, 2535397941156689968365568000000, 5316967764024635660932200566930538496, 44601618005626665627415483458173009920000000

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: A363423 A102922 A139688 * A292416 A304985 A292814

Adjacent sequences: A197353 A197354 A197355 * A197357 A197358 A197359

Keyword

nonn

Author

Geoffrey Critzer, Oct 14 2011

Status

approved