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A228859 Triangular array read by rows. T(n,k) is the number of labeled bipartite graphs on n nodes having exactly k connected components; n>=1, 1<=k<=n. 1
1, 1, 1, 3, 3, 1, 19, 15, 6, 1, 195, 125, 45, 10, 1, 3031, 1545, 480, 105, 15, 1, 67263, 27307, 7035, 1400, 210, 21, 1, 2086099, 668367, 140098, 24045, 3430, 378, 28, 1, 89224635, 22427001, 3746925, 536214, 68355, 7434, 630, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The Bell transform of A001832(n+1) (without column 0). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 21 2016

LINKS

Table of n, a(n) for n=1..45.

FORMULA

E.g.f.: sqrt(A(x)^y) where A(x) is the e.g.f. for A047863.

Sum_{k=1..n} T(n,k)*2^k = A047863(n).

EXAMPLE

1,

1, 1,

3, 3, 1,

19, 15, 6, 1,

195, 125, 45, 10, 1,

3031, 1545, 480, 105, 15, 1,

MATHEMATICA

nn=9; f[x_]:=Sum[Sum[Binomial[n, k]2^(k(n-k)), {k, 0, n}]x^n/n!, {n, 0, nn}]; Map[Select[#, #>0&]&, Drop[Range[0, nn]!CoefficientList[Series[Exp[y Log[f[x]]/2], {x, 0, nn}], {x, y}], 1]]//Grid

PROG

(Sage) # uses[bell_matrix from A264428, A001832]

# Adds 1, 0, 0, 0, ... as column 0 to the triangle.

bell_matrix(lambda n: A001832(n+1), 8) # Peter Luschny, Jan 21 2016

CROSSREFS

Row sums are A047864.

Column 1 is A001832.

Cf. A047863.

Sequence in context: A108391 A111840 A174031 * A259876 A276402 A318110

Adjacent sequences:  A228856 A228857 A228858 * A228860 A228861 A228862

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Sep 05 2013

STATUS

approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)