1468457

Properties

Appears in sequences

• a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.at n=9A000255
• Triangle read by rows: T(n,k) is the number of permutations of [n] having k consecutive ascending pairs (0 <= k <= n-1).at n=54A010027
• Irregular triangle read by rows: T(n,k) (n>=1, 0 <= k <= floor(n/2)) = number of permutations of 1..n with exactly floor(n/2) - k runs of consecutive pairs up.at n=34A010029
• 9th differences of factorial numbers.at n=1A023046
• Numerator of Sum_{k=0..n} (-1)^k/k!.at n=11A053557
• Triangular array formed from successive differences of factorial numbers, then with factorials removed.at n=64A060475
• Bisection of A000255.at n=4A100445
• First differences of the rows in the triangle of A116853, starting with 0.at n=45A116854
• Triangle read by rows: T(n,k) is the number of permutations of [n] having k small descents (n >= 1; 0 <= k <= n-1). A small descent in a permutation (x_1,x_2,...,x_n) is a position i such that x_i - x_(i+1) = 1.at n=45A123513
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k maximal strings of increasing consecutive integers (0<=k<=floor(n/2)).at n=30A136123
• Largest prime factor in the subfactorial of n.at n=8A152024
• Number of permutations of {1,2,...,n} in which the fixed points and the non-fixed points alternate.at n=19A162969
• Numerator of n!*Sum((-1)^k/k!, k=0..n)/(n-1)^n.at n=9A178453
• Triangle read by rows: T(n,k) is the number of permutations of [n] having no 3-sequences and having k successions (0 <= k <= floor(n/2)); a succession of a permutation p is a position i such that p(i +1) - p(i) = 1.at n=30A180185
• Triangle read by rows: T(n,k) is the number of permutations of [n] having k blocks of odd length (0<=k<=n).at n=63A180193
• Triangle read by rows: T(n,k) is the number of permutations of [n] that have k isolated entries (0 <= k <= n).at n=65A180196
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} whose longest block is of length k (0<=k<=n).at n=56A184182
• Triangle read by rows, T(n,k) n>=0, k>=0, generalization of A000255.at n=45A216154
• Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.at n=45A321711
• Array read by upwards antidiagonals: T(n,k) is the number of ways to place n persons on different seats such that each person number p, 1 <= p <= n, differs from the seat number s(p), 1 <= s(p) <= n+k, k >= 0.at n=46A336246