A201968 Limiting number of graphs with m+n nodes and m connected components as m tends to infinity.

1, 1, 3, 9, 33, 157, 1077, 12562, 276361, 12023304, 1019341931, 165104554019, 50503104222056, 29054325051128443, 31426537149908636858, 64001044963441537716700, 245935895697060179316310623, 1787577789272803153324620542087, 24637809499317378365431171138790458

Offset: 0

Author

Max Alekseyev, Dec 07 2011

Keywords

• nonn

Formula

Limit of A201922(m+n,m) as m tends to infinity.

a(n) = A201922(2*n,n) = A201922(2*n+1,n+1) = ...

a(n) = sum over the partitions of n of Product_{i=1..n} binomial(A001349(i+1)+Ki-1, Ki), where Ki is the number of parts equal to i, 1*K1 + 2*K2 + ... + n*Kn = n.