A122801 Number of labeled bipartite graphs on 2n vertices having equal parts and no isolated vertices.

1, 1, 21, 2650, 1452605, 3149738046, 26503552820514, 868081172737564500, 111606080497500509325405, 56762846667123360827351083510, 114847831981827229530824587617895286, 927685362544629192461621864598358779955500, 29976424929810726580224613882836823991388901138994

Offset: 0

Author

Max Alekseyev, Sep 11 2006

Keywords

• nonn

Links

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

Crossrefs

Cf. A122802, A048291, A052332, A001831, A002031, A047863, A001700.

Programs

PARI

{ A122801(n) = binomial(2*n-1,n) * sum(k=0, n, binomial(n, k) * (-1)^k * (2^(n-k)-1)^n ); }

Formula

For n>0, a(n) = A001700(n-1) * A048291(n) = A052332(2n) - A122802(2n).

Extensions

Terms a(11) and beyond from Andrew Howroyd, Nov 07 2019