Sequences

Number of singular n X n rational (0,1)-matrices.

Generalized tangent numbers d(6,n).

Number of bipartite partitions of n white objects and 3 black ones.

Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)*Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives A(A000092(n)).

Numbers that are the sum of 4 nonzero squares.

Numbers that are the sum of 2 but no fewer nonzero squares.

Number of 6-dimensional partitions of n.

Euler transform of A000389.

Number of n-node rooted trees of height 7.

Numbers that are the sum of 3 but no fewer nonzero squares.

Powers of 7: a(n) = 7^n.

Number of isomorphism classes of connected 3-regular (trivalent, cubic) loopless multigraphs of order 2n.

Concatenation of numbers from n down to 1.

a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.

Differences of reciprocals of unity.

Coefficients of ménage hit polynomials.

Coefficients of ménage hit polynomials.

Number of 7-dimensional partitions of n.

Euler transform of A000579.

Number of n-node rooted trees of height 8.

Primes and squares of primes.

Expansion of 2*x^3/((1-2*x)^2*(1-4*x)).

Series-parallel numbers.

n written in base where place values are positive cubes.

Number of permutations of [n] in which the longest increasing run has length 4.

Normalized total height of all nodes in all rooted trees with n labeled nodes.

Generalized Euler numbers c(3,n).

Smallest nonnegative number that is the sum of 3 squares in exactly n ways.

Number of 1-factorizations of complete graph K_{2n}.

Powers of rooted tree enumerator.

Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-4 places.

a(n) = Sum_{k=1..n-1} k*sigma(k)*sigma(n-k).

a(n) = (n!)^3.

Numbers that are the sum of 2 squares in exactly 3 ways.

Number of partially labeled rooted trees with n nodes (3 of which are labeled).

Latest possible occurrence of the first consecutive pair of n-th power residues, modulo any prime.

Smallest number that is the sum of 2 squares (allowing zeros) in exactly n ways.

a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.

Smallest number that is the sum of 2 squares in at least n ways.

Rencontres numbers: number of permutations of [n] with exactly 3 fixed points.

Coefficients of ménage hit polynomials.

Smallest number that is the sum of 3 squares in at least n ways.

The greedy sequence of integers which avoids 3-term geometric progressions.

Stirling numbers of the second kind, S(n,4).

Unsigned Stirling numbers of first kind s(n,4).

Digits of powers of 2.

Number of permutations of [n] in which the longest increasing run has length 5.

Exponential generating function: (1+3*x)/(1-2*x)^(7/2).

a(0) = a(1) = 1; thereafter a(n) = sigma(a(n-1)) + sigma(a(n-2)).

Number of multiset permutations of {1, 1, 2, 2, ..., n, n} with no fixed points.