273343

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=9A003319
• Array T(n,k) = number of subgroups of index k in free group of rank n, read by antidiagonals.at n=43A049290
• 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=36A059438
• Triangle read by rows. T(n, k) = A059438(n, k) for 1 <= k <= n, and T(n, 0) = n^0.at n=46A085771
• 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=36A104980
• 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=47A104980
• Triangle read by rows: number of atomic set compositions of size n and length k (see description in A095989) 1 <= k <= n.at n=44A109062
• Square table, read by antidiagonals, where the g.f. for row n+1 is generated by: x*R_{n+1}(x) = (1+n*x - 1/R_n(x))/(n+1) with R_0(x) = Sum_{n>=0} n!*x^n.at n=53A111528
• Triangle T(n,k) = A000142(n-k)*A003319(k+1) read by rows.at n=44A141476
• 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=36A156628
• 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=47A156628
• G.f. A(x) satisfies: [x^n] A(x)^n = [x^n] A(x)^(n-1) for n>1 with A(0)=A'(0)=1.at n=9A158882
• Triangle T(n,k), read by rows, given by (1,2,2,3,3,4,4,5,5,6,6,...) DELTA (1,0,1,0,1,0,1,0,1,0,1,0,1,...) where DELTA is the operator defined in A084938.at n=36A200659
• Rectangular table where the g.f. of row n satisfies: R(n,x) = 1 + x*R(n,x)^n * [d/dx x/R(n,x)] for n>=0, as read by antidiagonals.at n=64A208896
• A recurrent sequence in Panaitopol's formula for pi(x), where pi(x) is the number of primes <= x.at n=8A233824
• 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=44A263484
• Bisection of A003319: a(n) = A003319(2n+1).at n=4A272657
• 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=35A370380
• 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=35A370381