109601

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=8A000522
• Numerator of Sum_{k=0..n} 1/k!.at n=8A061354
• Triangle T(n,k) read by rows, where e.g.f. for T(n,k) is exp((1+y)*x)/(1-x).at n=36A073107
• Triangle T(n,k) read by rows, where o.g.f. for T(n,k) is n!*Sum_{k=0..n} (1+x)^(n-k)/k!.at n=36A073474
• Binomial triangle based on factorials.at n=44A076571
• Square array of numbers related to the incomplete gamma function, read by antidiagonals.at n=53A080955
• Transposed version of A080955: T(n,k) = A080955(k,n), n>=0, k>=-1.at n=63A089258
• 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=20A121579
• 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=29A121632
• Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and such that the sum of the bottom levels of all columns is k (n>=1, k>=0; informally, the number of the "missing" cells in the right bottom corner of the polyomino). 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=42A122104
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} in which the last entry of the first increasing run is equal to k (1 <= k <= n).at n=44A134433
• 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=46A134558
• Square array read by antidiagonals: form the Euler-Seidel matrix for the sequence {k!} and then divide column k by k!.at n=36A143409
• Square array read by antidiagonals upwards: T(n,k) is the number of scenarios for the gift exchange problem in which each gift can be stolen at most once, when there are n gifts in the pool and k gifts (not yet frozen) in peoples' hands.at n=53A144502
• Array described in comments to A053482, here read by increasing antidiagonals. See comments below.at n=57A181783
• 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=54A191490
• Squarefree part of the total number of arrangements of a set with n elements.at n=8A222637
• Pairs p, q for those partial sums p/q of the series e = sum_{n>=0} 1/n! that are not convergents to e.at n=12A233044
• Triangular array of coefficients of polynomials p(n,k) defined in Comments.at n=36A248664
• Triangular array of coefficients of polynomials q(n,k) defined in Comments.at n=36A248669