317520

Appears in sequences

• Number of simplices in barycentric subdivision of n-simplex.at n=5A005461
• Triangular array a(n,k) = (1/k)*Sum_{i=0..k} (-1)^(k-i)*binomial(k,i)*i^n; n >= 1, 1 <= k <= n, read by rows.at n=41A028246
• Number of ways to partition n labeled elements into 6 pie slices.at n=3A032180
• Number of labeled rooted trees with a degree constraint: (2*n)!/(2^n) * C(2*n+1, n).at n=4A036770
• a(0)=0, for n >= 1, a(n) = (2^(n-1)-1)*n!.at n=7A052665
• Number of k-simplices in the first derived complex of the standard triangulation of an n-simplex. Equivalently, T(n,k) is the number of ascending chains of length k+1 of nonempty subsets of the set {1, 2, ..., n+1}.at n=32A053440
• Number of step shifted (decimated) sequences using exactly six different symbols.at n=8A056380
• Number of primitive (aperiodic) step shifted (decimated) sequences using exactly six different symbols.at n=8A056390
• Coefficient triangle of generalized Laguerre polynomials n!*L(n,2,x) (rising powers of x).at n=30A062139
• Triangle T(n,k), 0<=k<=n, read by rows, defined by : T(0,0) = 1, T(n,k) = 0 if n<k or if k<0, T(n,k) = k*T(n-1, k-1) + (2n-2k-1)*T(n-1, k).at n=39A108032
• Triangle T(n,k), the number of permutations on n elements that have no cycles of length k.at n=43A122974
• a(n) = n*(n+2)*n!.at n=7A130744
• Triangle read by rows, 0 <= k <= n, T(n,k) = Sum_{j=0..n} A(n,j)*binomial(n-j,k) where A(n,j) are the Eulerian numbers A173018.at n=39A130850
• Triangle T(n, k) = n*( (n-1)! - (k-1)! ), read by rows.at n=43A137259
• Expansion of the exponential generating function 1 - log(1 - x*(exp(z) - 1)), triangle read by rows, T(n,k) for n >= 0 and 0 <= k <= n.at n=51A142071
• Triangle read by rows: T(n,m) = A094310(n,m)*A120070(n+1,m), 1 <= m <= n.at n=21A165969
• Triangle T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = 12*Product_{j=3..n} ( 12 * binomial(j+2, 4) ) with c(0) = c(1) = 1, read by rows.at n=38A174151
• Triangle T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = 12*Product_{j=3..n} ( 12 * binomial(j+2, 4) ) with c(0) = c(1) = 1, read by rows.at n=42A174151
• Irregular triangle T(n,k) = A096162(n,k) * A036040(n,k) * A048996(n,k) * A098546(n,k) * A178886(n,k), read by rows, 1 <= k <= A000041(n).at n=34A179236
• Augmentation of the triangular array P=A130296 whose n-th row is (n+1,1,1,1,1...,1) for 0<=k<=n. See Comments.at n=38A193094