109584

Appears in sequences

• Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.at n=8A000254
• Triangle read by rows of differences of reciprocals of unity.at n=29A008969
• Triangle of "Harmonic Coefficients" T(n,k), read by rows: (Sum_{i=1..n} T(n,i) * k^i) * k! / ((n+k)! * n!) = (Sum_{i=1..k} (1/i-1/(i+n)) = n * (Sum_{i=1..k} 1/(i*(i+n)))).at n=35A027858
• McKay-Thompson series of class 13A for the Monster group with a(0) = -2.at n=19A034318
• McKay-Thompson series of class 13A for the Monster group with a(0) = 0.at n=19A034319
• A triangle of generalized Stirling numbers: sum of consecutive terms in the harmonic sequence multiplied by the product of their denominators.at n=36A067176
• Triangle of coefficients, read by rows, where the n-th row forms the polynomial P(n,x) = {Sum_{k=1..n} 1/(k+x)}*{Product_{k=1..n} (k+x)}.at n=28A074246
• Triangle read by rows: for 0 <= k < n, a(n, k) is the sum of the products of all subsets of {n-k, n-k+1, ..., n} with k members.at n=35A093905
• Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the unsigned Stirling numbers of the first kind in reverse order).at n=43A094638
• a(n) = (Sum 1/k) (Product k), where both the sum and product are over those k where 1 <= k <= n/2 and gcd(k,n) = 1.at n=15A099001
• Array read by descending antidiagonals: A(n, k) = (n + 1)! * H(k, n + 1), where H(n, k) is a higher-order harmonic number, H(0, k) = 1/k and H(n, k) = Sum_{j=1..k} H(n-1, j), for 0 <= k <= n.at n=43A105954
• Triangle read by rows: a(n, n) = n! and for 1 <= k < n, a(n, k) = Sum_{i=0..n-1} Product_{j=i+1..i+k} f(j, n), where for x <= y, f(x, y) = x and for x > y, f(x, y) = x-y.at n=34A109876
• Eighth column of triangle A112492 (inverse scaled Pochhammer symbols).at n=1A111888
• Triangle from inverse scaled Pochhammer symbols.at n=43A112492
• Alfred Moessner's factorial triangle.at n=29A125714
• Triangle read by rows: row n (n>=0) has g.f. Sum_{i=1..n} n!*x^i*(1+x)^(n-i)/(n+1-i).at n=44A126671
• Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increasing powers of x. T(n,k) is also the unsigned Stirling number |s(n+1, k+1)|, denoting the number of permutations on n+1 elements that contain exactly k+1 cycles.at n=37A130534
• Sum of all n-digit Stirling numbers of first kind.at n=5A131014
• Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n.at n=47A132393
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} whose 2nd cycle has k entries; each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements (n>=1; 0<=k<=n-1). For example, 1432=(1)(24)(3) has 2 entries in the 2nd cycle; 3421=(1324) has 0 entries in the 2nd cycle.at n=37A138771