680400

Appears in sequences

• Expansion of e.g.f.: -x^3*(log(1-x))^3.at n=9A052786
• Number T(n,m) of n X m matrices over {0,1,2} with all row and column sums equal to 1 or 2, m=0,..,2*n.at n=34A062154
• a(n) = (n-1)!(n+2)!/(3*2^n).at n=6A067550
• This table shows the coefficients of combinatorial formulas needed for generating the sequential sums of p-th powers of triangular numbers. The p-th row (p>=1) contains a(i,p) for i=1 to 2*p-1, where a(i,p) satisfies Sum_{i=1..n} C(i+1,2)^p = 3 * C(n+2,3) * Sum_{i=1..2*p-1} a(i,p) * C(n-1,i-1)/(i+2).at n=34A087127
• Denominators used in the computation of the column sequences of array A078739 ((2,2)-Stirling2).at n=9A089512
• a(n) = (n+1)*(2*n)!/2^n.at n=5A132911
• Triangle T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2, read by rows.at n=47A156995
• Triangle T(n, k, q) = n!*(n+1)!*q^k/((n-k)!(n-k+1)!) if floor(n/2) > k-1, otherwise n!*(n+1)!*q^(n-k)/(k!*(k+1)!) for q = 3, read by rows.at n=24A174451
• Number of permutations of 1..n with the sequence of sums of 5 adjacent elements having exactly 1 maximum.at n=6A179724
• Number of permutations of 1..n with the sequence of sums of 5 adjacent elements having exactly 3 maxima.at n=2A179726
• Number of (n+1)X2 0..5 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.at n=3A203710
• Number of (n+1)X5 0..5 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.at n=0A203713
• T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.at n=6A203714
• T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.at n=9A203714
• Triangle read by rows: terms of a binomial decomposition of 1 as Sum(k=0..n)T(n,k).at n=33A244119
• a(n) is the smallest number k for which k and the arithmetic derivative k' (A003415) have exactly n triangular divisors (A000217).at n=16A357842
• Number of permutations of [n] such that the element sum of each cycle is odd.at n=10A369080
• Numbers k with squarefree kernel 210 such that both k-1 and k+1 are prime.at n=30A392030