33880

Appears in sequences

• Expansion of (1-x)^(-3) * (1-x^2)^(-2).at n=39A002624
• a(n) = n*(n+1)*(n+2)^2/6.at n=20A004320
• Gaussian binomial coefficient [ n,3 ] for q=3.at n=3A006101
• Gaussian binomial coefficient [ 2n,n ] for q=3.at n=3A006103
• Gaussian binomial coefficient [ n,n/2 ] for q=3.at n=6A006104
• Number of singular 2 X 2 matrices over Z(n) (i.e., with determinant = 0).at n=27A020478
• Triangle of Gaussian binomial coefficients [ n,k ] for q = 3.at n=24A022167
• Number of sublattices of index n in generic 4-dimensional lattice.at n=26A038991
• Triangular array T(n,k) giving number of weakly connected digraphs with n labeled nodes and k arcs (n >= 1, 0 <= k <= n(n-1)).at n=30A062735
• a(n) = Z(S_m; sigma[1](n), sigma[2](n),..., sigma[m](n)) where Z(S_m; x_1,x_2,...,x_m) is the cycle index of the symmetric group S_m and sigma[k](n) is the sum of k-th powers of divisors of n; m=3.at n=26A068020
• Triangle read by rows: T(n,k) is number of leaves at level k in all noncrossing rooted trees on n+1 nodes.at n=31A101372
• Square array T(n, k) = q-binomial(2*n, n, k+1), read by antidiagonals.at n=18A156914
• General q-Narayana triangle sequence: T(n, k) = Product_{j=0..2} ( q_binomial(n+j, j+k, 3)/q_binomial(n+j-k, j, 3) ).at n=11A156917
• General q-Narayana triangle sequence: T(n, k) = Product_{j=0..2} ( q_binomial(n+j, j+k, 3)/q_binomial(n+j-k, j, 3) ).at n=13A156917
• G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^A038722(n), where A038722(n) = floor(sqrt(2*n)+1/2)^2 - n + 1.at n=21A192316
• Triangular array read by rows: T(n,k) is the number of functional digraphs on {1,2,...,n} such that every element is mapped to a recurrent element and there are exactly k cycles, n>=1, 1<=k<=n.at n=32A228534
• Number T(n,k) of n-step walks on cubic lattice starting at (0,0,0), ending at (0,k,n-k) and using steps (0,0,1), (0,1,0), (1,0,0), (-1,1,1), (1,-1,1), and (1,1,-1); triangle T(n,k), n>=0, 0<=k<=n, read by rows.at n=40A328347
• Number of 2n-step walks on cubic lattice starting at (0,0,0), ending at (0,n,n) and using steps (0,0,1), (0,1,0), (1,0,0), (-1,1,1), (1,-1,1), and (1,1,-1).at n=4A328426
• a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 3 even numbers.at n=44A330299
• a(n) is the number of subsets of {1..n} that contain exactly 3 odd and 1 even numbers.at n=44A333319