69264

Appears in sequences

• Generalized Stirling numbers, [n+2,3]_2: a(n) = n! * Sum_{k=0..n-1} (k+1)/(n-k).at n=7A001705
• Theta series of E_6 lattice.at n=31A004007
• Generalized Stirling number triangle of first kind.at n=29A049444
• A triangle of generalized Stirling numbers: sum of consecutive terms in the harmonic sequence multiplied by the product of their denominators.at n=37A067176
• Triangle of labeled rooted trees according to the number of increasing edges.at n=29A067948
• Triangle of labeled rooted trees according to the number of increasing edges.at n=34A067948
• 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=34A093905
• 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=42A105954
• Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have k pyramids of the first kind (a pyramid of the first kind is a sequence u^pd^p for some positive integer p, starting at the x-axis).at n=29A108451
• a(n) = denominator of sum of reciprocals of the terms of the continued fraction for H(n) = Sum_{k=1..n} 1/k.at n=41A112287
• Coefficient triangle for polynomials used for e.g.f.s for unsigned Stirling1 diagonals.at n=29A112486
• a(n) = (2*n+1)^n-(2*n-1)^n-(2*n)^n.at n=6A127691
• Triangle read by rows: T(n,k) = (-1)^(n+k)*Sum_{j=1..k} s(n,j), where s(n,j) are the signed Stirling numbers of the first kind (n >= 2; 1 <= k <= n-1; s(n,j) = A008275(n,j)).at n=29A136124
• 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=38A138771
• Triangle read by rows: T(n,k) is the number of white corners of rank k in all the permutations of {1,2,...,n} (n>=2, 0<=k<=n-2; for definitions see the Eriksson-Linusson references).at n=21A140713
• Unsigned 2-Stirling numbers of the first kind.at n=29A143491
• Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....at n=34A145324
• Triangle generated by the asymptotic expansions of the E(x,m=2,n).at n=29A165674
• Triangle read by rows. T(n, k) = (n - k + 1)! * H(k, n - k), where H are the hyperharmonic numbers. For 0 <= k <= n.at n=38A165675
• Seventh right hand column of triangle A165674.at n=1A165679