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

2,2

Links

G. C. Greubel, Table of n, a(n) for the first 10 rows, flattened

Eric Weisstein's World of Mathematics, Proper Cover.

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).

Example

1;
6,17,15,6,1;
25,230,861,1918,2975,3428,3003,2002,1001,364,91,14,1;
...

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 *)

Prog

(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

Crossrefs

Cf. A007537(row sums), A055154, A055127, A055152, A095422, A095423.

Sequence in context: A070395 A200871 A112366 * A063584 A019296 A035484

Adjacent sequences: A095418 A095419 A095420 * A095422 A095423 A095424

Keyword

easy,nonn,tabf

Author

Goran Kilibarda, Vladeta Jovovic, Jun 04 2004

Status

approved