2829325

Appears in sequences

• Number of connected permutations of [1..n] (those not fixing [1..j] for 0 < j < n). Also called indecomposable permutations, or irreducible permutations.at n=10A003319
• Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) is the number of permutations of [1..n] with k components.at n=45A059438
• Triangle read by rows. T(n, k) = A059438(n, k) for 1 <= k <= n, and T(n, 0) = n^0.at n=56A085771
• Triangular matrix T, read by rows, that satisfies: SHIFT_LEFT(column 0 of T^p) = p*(column p+1 of T), or [T^p](m,0) = p*T(p+m,p+1) for all m>=1 and p>=-1.at n=45A104980
• Square array, read by antidiagonals, where row n+1 is generated from row n by first removing terms in row n at positions 0 and {(m+1)*(m+2)/2-2, m>0} and then taking partial sums, starting with all 1's in row 0.at n=45A156628
• A recurrent sequence in Panaitopol's formula for pi(x), where pi(x) is the number of primes <= x.at n=9A233824
• Triangle read by rows: T(n,k) (n>=1, 0<=k<n) is the number of permutations of n elements with n-k elements in its connectivity set.at n=54A263484
• Bisection of A003319: a(n) = A003319(2n).at n=5A272656
• Array read by downward antidiagonals: A(n,k) = (k+2)*A(n-1,k+1) + Sum_{j=0..k} A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.at n=44A370380
• Array read by downward antidiagonals: A(n,k) = Sum_{j=0..k+1} binomial(k+2, j+1)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.at n=44A370381