204630

Appears in sequences

• Number of simplices in barycentric subdivision of n-simplex.at n=3A005464
• a(n) = 4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1 (essentially Stirling numbers of second kind).at n=9A028244
• 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=48A028246
• 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=38A053440
• 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=51A075263
• 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=51A130850
• Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.at n=29A200166
• a(n) = binomial(n^2,3)/(2*n).at n=18A201106
• Third differences of ninth powers (A001017).at n=3A255183
• 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=49A285867
• 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=59A298668
• a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=3, a(1)=10, a(2)=26.at n=14A316937
• Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^3 ).at n=10A366096