27203

Appears in sequences

• Poincaré series [or Poincare series] for depths of roots in a certain root system.at n=26A019527
• a(n) = Sum_{k=0..n} C(n,k)*S2(n,k). Binomial convolution of the Stirling numbers of the 2nd kind. Also sum of the rows of A122454.at n=7A122455
• Triangle, read by rows, where T(n,k) = [(I + D*C)^n](n,k); that is, row n of T = row n of (I + D*C)^n for n>=0 where C denotes Pascal's triangle, I the identity matrix and D a matrix where D(n+1,n)=1 and zeros elsewhere.at n=28A134090
• a(n) = 225*n^2 - 2*n.at n=10A158226
• Number of 2X3 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 2 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).at n=22A192698
• Principal diagonal of the convolution array A213836.at n=21A213837
• Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j-1,-n-1)*S2(k,j), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n.at n=35A271702
• Number of ways to split an integer partition of n into consecutive subsequences with weakly decreasing sums.at n=19A316245
• a(n) is the largest number that can be expressed as the sum of three positive triangular numbers in exactly n ways.at n=19A330811