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A055192 Number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block, up to isomorphism. 7
1, 2, 5, 12, 35, 108, 393, 1666, 8543, 54190, 436740, 4565450, 62930604, 1156277748, 28509174012, 946786816168, 42448800498744, 2573207315483554, 211180300735118954, 23490473719472829824, 3545759835559406756008, 727077827560669587718290 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Also the number of connected split graphs on n vertices (cf. A048194). - Falk Hüffner, Dec 01 2015

Inverse Euler transform is A007776. - Andrew Howroyd, Oct 03 2018

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..40

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Flatten @ Table[ Map[ Function[{p}, p + j*x^i], b[n - i*j, i - 1]], {j, 0, n/i}]]];

g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}];

A[n_, k_] := g[Min[n, k], Abs[n - k]];

A049312[d_] := Sum[A[n, d - n], {n, 0, d}];

Differences[Table[A049312[n], {n, 0, 23}], 2] (* Jean-François Alcover, Sep 05 2019, after Alois P. Heinz in A049312 *)

CROSSREFS

Equals second differences of A049312.

Cf. A007776, A024206, A055609, A055082, A055083, A055084.

Row sums of A056152 and also of A122083.

Sequence in context: A000104 A342537 A000105 * A108555 A323397 A292169

Adjacent sequences:  A055189 A055190 A055191 * A055193 A055194 A055195

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 18 2000

STATUS

approved

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Last modified April 13 01:36 EDT 2021. Contains 342934 sequences. (Running on oeis4.)