94828

Appears in sequences

• 2-Bell numbers: a(n) = number of partitions of [n+1] with a distinguished block.at n=8A005493
• Aitken's array: triangle of numbers {a(n,k), n >= 0, 0 <= k <= n} read by rows, defined by a(0,0)=1, a(n,0) = a(n-1,n-1), a(n,k) = a(n,k-1) + a(n-1,k-1).at n=53A011971
• Sequence formed by reading rows of triangle defined in A011971.at n=44A011972
• Triangle of numbers a(n,k), 0 <= k <= n: number of set partitions of {1,2,...,n} in which exactly k of the blocks have been distinguished.at n=46A049020
• Triangle T(n,k) is the number of restricted growth strings (RGS) of set partitions of {1..n} that have an increase at index k (1<=k<n).at n=36A056861
• Triangle T(n,k) is the number of restricted growth strings (RGS) of set partitions of {1..n} that have a decrease at index k (1<=k<n).at n=46A056862
• Triangle read by rows. T(n, k) = Sum_{i=0..n} Stirling2(n, i)*Product_{j=1..k} (i - j + 1) for 0 <= k <= n.at n=46A059098
• Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318).at n=36A095675
• Array, read by antidiagonals, where A(n,k) = exp(-1)*Sum_{i>=0} (i+k)^n/i!.at n=57A108087
• Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the last block is the singleton {k}, 1<=k<=n; the blocks are ordered with increasing least elements.at n=64A108458
• Mirror image of the Bell triangle A011971, which is also called the Pierce triangle or Aitken's array.at n=46A123346
• Number of embedded coalitions in an n-person game.at n=8A138378
• Word structures of length n using a 10-ary alphabet, including a special character, which may occur in the leftmost word position only if n=1.at n=9A164933
• Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.at n=37A244489
• Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most nine elements.at n=10A276725
• Number T(n,k) of blocks of size >= k in all set partitions of [n], assuming that every set partition contains one block of size zero; triangle T(n,k), n>=0, 0<=k<=n, read by rows.at n=46A283424