A122802 Number of labeled bipartite graphs on n vertices with no isolated vertices.

1, 0, 1, 6, 29, 510, 5032, 161406, 3294405, 194342910, 7934652356, 881008805886, 71275547085536, 15178191426486270, 2434250064518832302, 1008694542117649154046, 321680912414994434144165, 262063364967549826752315390, 166681427053102507699172431372

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

a(2n+1) = A052332(2n+1); a(2n) = A052332(2n) - A122801(n) for n > 0.

Prog

(PARI) a(n)={sum(k=0, n, binomial(n, k)*(2^k-2)^(n-k)) - if(n%2==0&&n>0, binomial(n-1, n/2)*sum(k=0, n/2, binomial(n/2, k)*(-1)^k*(2^(n/2-k)-1)^(n/2)))} \\ Andrew Howroyd, Nov 07 2019

Crossrefs

Cf. A122801, A052332, A001831, A002031, A047863.

Sequence in context: A344434 A321141 A359053 * A144746 A051685 A326858

Adjacent sequences: A122799 A122800 A122801 * A122803 A122804 A122805

Keyword

nonn

Author

Max Alekseyev, Sep 11 2006

Extensions

Terms a(17) and beyond from Andrew Howroyd, Nov 07 2019

Status

approved