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A121933 Number of labeled digraphs with n arcs for which every vertex has indegree at least one and outdegree at least one. 2
1, 0, 1, 2, 18, 158, 1788, 23930, 370886, 6527064, 128542420, 2800362536, 66858556196, 1735834171276, 48689118113374, 1467253017578672, 47275138863637080, 1621757692715997136, 59013695834307968254, 2270400832166224741596, 92078072790064946096284 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..60

FORMULA

G.f.: Sum(Sum((-1)^(n-k)*binomial(n,k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k),k=0..n),n=0..infinity).

a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.0722246614111436... . - Vaclav Kotesovec, May 07 2014

In closed form, c = 1/(sqrt(Pi*(1-log(2))) * log(2) * 2^(4+log(2)/2)). - Vaclav Kotesovec, May 04 2015

MAPLE

n:=20: t:=taylor(sum(sum((-1)^(m-k)*binomial(m, k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(m-k), k=0..m), m=0..n), x, n+1): seq(coeff(t, x, m), m=0..n); # Nathaniel Johnston, Apr 28 2011

MATHEMATICA

Flatten[{1, Rest[CoefficientList[Series[Sum[Sum[(-1)^(n-k)*Binomial[n, k]*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k), {k, 0, n}], {n, 1, 20}], {x, 0, 20}], x]]}] (* Vaclav Kotesovec, May 07 2014 *)

CROSSREFS

Cf. A121252, A086193.

Sequence in context: A191814 A052838 A052876 * A108550 A322282 A270369

Adjacent sequences:  A121930 A121931 A121932 * A121934 A121935 A121936

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 02 2006

STATUS

approved

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Last modified September 23 08:09 EDT 2020. Contains 337295 sequences. (Running on oeis4.)