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A209324 Triangular array read by rows: T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} whose largest component has exactly k nodes; n>=1, 1<=k<=n. 1
1, 1, 3, 1, 9, 17, 1, 45, 68, 142, 1, 165, 680, 710, 1569, 1, 855, 6290, 8520, 9414, 21576, 1, 3843, 47600, 134190, 131796, 151032, 355081, 1, 21819, 481712, 1838900, 2372328, 2416512, 2840648, 6805296, 1, 114075, 5025608, 21488292, 50609664, 48934368, 51131664, 61247664, 148869153 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Here component means weakly connected component in the functional digraph of f.

Row sums are n^n.

T(n,n) = A001865.

REFERENCES

R. Sedgewick and P. Flajolet, Analysis of Algorithms, Addison and Wesley, 1996, Chapter 8.

LINKS

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

FORMULA

E.g.f. for column k:  exp( Sum_{n=1..k} A001865(n) x^n/n!) - exp( Sum_{n=1..k-1} A001865(n) x^n/n!).

EXAMPLE

1;

1, 3;

1, 9,     17;

1, 45,    68,     142;

1, 165,   680,    710,     1569;

1, 855,   6290,   8520,    9414,    21576;

1, 3843,  47600,  134190,  131796,  151032,  355081;

1, 21819, 481712, 1838900, 2372328, 2416512, 2840648, 6805296;

MATHEMATICA

nn=8; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; c=Log[1/(1-t)]; b=Drop[Range[0, nn]!CoefficientList[Series[c, {x, 0, nn}], x], 1]; f[list_]:=Select[list, #>0&]; Map[f, Drop[Transpose[Table[Range[0, nn]!CoefficientList[Series[ Exp[Sum[b[[i]]x^i/i!, {i, 1, n+1}]]-Exp[Sum[b[[i]]x^i/i!, {i, 1, n}]], {x, 0, nn}], x], {n, 0, nn-1}]], 1]]//Grid

CROSSREFS

Sequence in context: A056843 A076806 A111568 * A121489 A118793 A247231

Adjacent sequences:  A209321 A209322 A209323 * A209325 A209326 A209327

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Jan 19 2013

STATUS

approved

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Last modified February 23 07:03 EST 2019. Contains 320411 sequences. (Running on oeis4.)