166824

Appears in sequences

• Number of simplices in barycentric subdivision of n-simplex.at n=4A005462
• a(n) = 5^(n-1) - 4*4^(n-1) + 6*3^(n-1) - 4*2^(n-1) + 1 (essentially Stirling numbers of second kind).at n=8A028245
• 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=40A028246
• 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=31A053440
• Triangle of coefficients of polynomials H(n,x) formed from the first (n+1) terms of the power series expansion of ( -x/log(1-x) )^(n+1), multiplied by n!.at n=40A075263
• 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=40A130850
• 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=50A142071
• Triangle read by rows: The n-th derivative of the logistic function written in terms of y, where y = 1/(1 + exp(-x)).at n=40A163626
• G.f. A(x) = sum(n>0, a(n)*x^n/(2*n-1)!) is the inverse function to x*Bernoulli(x).at n=4A185157
• Triangle read by rows: the positive terms of A163626.at n=22A249163
• Triangle T(n, k) read by rows: T(n, k) = S2(n, k)*k! + S2(n, k-1)*(k-1)! with the Stirling2 triangle S2 = A048993.at n=41A285867
• Number T(n,k) of set partitions of [n] into k blocks such that the absolute difference between least elements of consecutive blocks is always > 1; triangle T(n,k), n>=0, 0<=k<=ceiling(n/2), read by rows.at n=60A298668