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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.)