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A055154 Triangle read by rows: T(n,k) = number of k-covers of a labeled n-set, k=1..2^n-1. 11
1, 1, 3, 1, 1, 12, 32, 35, 21, 7, 1, 1, 39, 321, 1225, 2919, 4977, 6431, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 1, 120, 2560, 24990, 155106, 711326, 2597410, 7856550, 20135050, 44337150, 84665490, 141118250, 206252550, 265182450, 300540190 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums give A003465.

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 165.

LINKS

Alois P. Heinz, Rows n = 1..10, flattened

FORMULA

T(n,k) = Sum_{j=0..n} (-1)^j*C(n, j)*C(2^(n-j)-1, k), k=1..2^n-1.

Also T(n,k) = (1/k!)*Sum_{j=0..k} Stirling1(k+1, j+1)*(2^j-1)^n. E.g.f.: Sum(exp(y*(2^n-1))*log(1+x)^n/n!, n=0..infinity)/(1+x). - Vladeta Jovovic, May 30 2004

Also exp(-y)*Sum((1+x)^(2^n-1)*y^n/n!, n=0..infinity).

EXAMPLE

[1], [1,3,1], [1,12,32,35,21,7,1], ...; There are 35 4-covers of a labeled 3-set.

MATHEMATICA

nn=5; Map[Select[#, #>0&]&, Transpose[Table[Table[Sum[(-1)^j Binomial[n, j] Binomial[2^(n-j)-1, m], {j, 0, n}], {n, 1, nn}], {m, 1, 2^nn-1}]]]//Grid (* Geoffrey Critzer, Jun 27 2013 *)

CROSSREFS

Cf. A054780, A055621.

Columns: A029858, A095152-A095155.

Sequence in context: A209424 A129619 A094573 * A015112 A174690 A156869

Adjacent sequences:  A055151 A055152 A055153 * A055155 A055156 A055157

KEYWORD

easy,nonn,tabf

AUTHOR

Vladeta Jovovic, Jun 14 2000

STATUS

approved

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Last modified April 22 08:06 EDT 2019. Contains 322329 sequences. (Running on oeis4.)