A095421 Triangle read by rows: T(n,m) = number of m-block proper covers (without empty blocks and without multiple blocks) of a labeled n-set (n>=2, 2<=m<=2^n-2).
1, 6, 17, 15, 6, 1, 25, 230, 861, 1918, 2975, 3428, 3003, 2002, 1001, 364, 91, 14, 1, 90, 2125, 20930, 127701, 568820, 2003635, 5820750, 14282125, 30030000, 54620475, 86490950, 119759325, 145422600, 155117515, 145422675, 119759850, 86493225
Offset: 2
Examples
1; 6,17,15,6,1; 25,230,861,1918,2975,3428,3003,2002,1001,364,91,14,1; ...
Links
- G. C. Greubel, Table of n, a(n) for the first 10 rows, flattened
- Eric Weisstein's World of Mathematics, Proper Cover.
Programs
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Mathematica
T[n_, m_] := Sum[(-1)^(n - i)*Binomial[n, i]*Binomial[2^i - 1, m], {i, 1, n}] - Binomial[2^n - 2, m - 1]; Table[T[n, m], {n, 2, 10}, {m, 2, 2^n - 2}] // Flatten (* G. C. Greubel, Oct 07 2017 *) -
PARI
for(n=2,6, for(m=2, 2^n -2, print1(sum(j=1,n, (-1)^(n-j)* binomial(n, j)*binomial(2^j -1, m)), ", "))) \\ G. C. Greubel, Oct 07 2017
Formula
T(n, m) = Sum((-1)^(n-i)*binomial(n, i)*binomial(2^i-1, m), i=1..n) - binomial(2^n-2, m-1).
Comments