986410

Appears in sequences

• Total number of ordered k-tuples (k=0..n) of distinct elements from an n-element set: a(n) = Sum_{k=0..n} n!/k!.at n=9A000522
• Triangle T(n,k) read by rows, where e.g.f. for T(n,k) is exp((1+y)*x)/(1-x).at n=45A073107
• Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having along the lower contour exactly k reentrant corners, i.e., a vertical step that is followed by a horizontal step (n>=1, k>=0).at n=25A121579
• Triangle read by rows: T(n,k) is the number of deco polyominoes of height n such that the bottom of the last column is at level k (n>=1; k>=0). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.at n=37A121632
• Array read by antidiagonals, a(n,k) = gamma(n+1,k)*e^k, where gamma(n,k) is the upper incomplete gamma function and e is the exponential constant 2.71828...at n=56A134558
• Square array read by antidiagonals: form the Euler-Seidel matrix for the sequence {k!} and then divide column k by k!.at n=45A143409
• Triangle generated by the recurrence T(n+1,k+1) = T(n,k+1) + n * T(n,k) + delta(n,k) with the initial values T(n,0) = 1 and T(0,k) = delta(k,0), where delta(n,k) is the Kronecker delta.at n=65A191490
• Squarefree part of the total number of arrangements of a set with n elements.at n=9A222637
• Triangular array of coefficients of polynomials q(n,k) defined in Comments.at n=45A248669
• Triangle read by rows: T(n,k) = logarithmic polynomial A_k^(n)(x) evaluated at x=-1.at n=45A260325
• a(n) = e*Gamma(2*n,1).at n=4A294039
• Number T(n,k) of permutations p of [n] such that k is the maximum of the partial sums of the signed up-down jump sequence of 0,p; triangle T(n,k), n>=0, ceiling((sqrt(1+8*n)-1)/2)<=k<=n, read by rows.at n=35A316292
• Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of the e.g.f. exp(x)/(1 - k*x).at n=64A320031
• Number of sequences of distinct ordered pairs of positive integers up to n.at n=3A326253
• Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(n,k) = n! * Sum_{j=0..n} j^k/j!.at n=54A337085
• Triangle read by rows: T(n,k) = Sum_{j=0..k} binomial(n,j) * j! (0 <= k <= n).at n=54A347667
• Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..n} binomial(n+(k-1)*j,k*j)/j!.at n=54A361600
• Nearest integer to e*n!.at n=9A370973
• Triangle read by rows: T(n, k) = e * binomial(n, k) * Gamma(k + 1, 1).at n=54A371686