A095421 -id:A095421 - cp's OEIS frontend

A095422 Triangle read by rows: T(n,m) = number of m-block proper T_0-covers (without empty blocks and without multiple blocks) of a labeled n-set (n>=2, 2<=m<=2^n-2).

1, 3, 17, 15, 6, 1, 0, 128, 771, 1882, 2969, 3428, 3003, 2002, 1001, 364, 91, 14, 1, 0, 420, 12845, 108731, 539105, 1969355, 5790720, 14262105, 30019990, 54616835, 86490040, 119759185, 145422590, 155117515, 145422675, 119759850, 86493225

Offset: 2

Goran Kilibarda, Vladeta Jovovic, Jun 04 2004

			1; 3,17,15,6,1; 0,128,771,1882,2969,3428,3003,2002,1001,364,91,14,1; ...

Cf. A095423(row sums), A095421.

T(n, m) = Sum(Stirling1(n+1, i+1)*binomial(2^i-1, m)-Stirling1(n, i)*binomial(2^i-2, m-1), i=1..n).

A095423 Number of proper T_0-covers of an n-set.

Original entry on oeis.org

0, 1, 42, 15654, 1073421588, 4611685989440629944, 85070591730234615704434641716516893512, 28948022309329048855892746252171976959574390130279817915318273546782086570304

Offset: 1

Goran Kilibarda, Vladeta Jovovic, Jun 04 2004

The next term has 154 decimal digits.

Row sums of A095422, A095421.

a(n)=sum(k=0,n, (2*stirling(n+1, k+1, 1) - stirling(n, k,1 )) * 2^(2^k-2) );
vector(10,n,a(n)) /* show terms */

a(n) = Sum(Stirling1(n, k)*A007537(k), k=1..n).

a(n) = Sum((2*Stirling1(n+1, k+1)-Stirling1(n, k))*2^(2^k-2), k=0..n).

cp's OEIS Frontend

A095422 Triangle read by rows: T(n,m) = number of m-block proper T_0-covers (without empty blocks and without multiple blocks) of a labeled n-set (n>=2, 2<=m<=2^n-2).

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A095423 Number of proper T_0-covers of an n-set.

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