Sequences

Eulerian numbers (Euler's triangle: column k=3 of A008292, column k=2 of A173018).

Concatenate n n times.

Numbers written in base of triangular numbers.

n followed by n^2.

Expansion of e.g.f. sin(x)/cos(2*x).

Number of bipartite partitions of n white objects and 4 black ones.

a(n) = 4*n^2 - 1.

Number of permutations of [n] in which the longest increasing run has length 6.

Powers of ten written in base 8.

1 together with products of 2 or more distinct primes.

Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-5 places.

a(n) = floor(sinh(n)).

a(n) = a(n-1)^2 + (a(n-2) + 1)*(a(n-1) - a(n-2)^2).

Number of genus 0 rooted maps with 5 faces and n vertices.

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

Rencontres numbers: number of permutations of [n] with exactly 4 fixed points.

Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-1 places.

a(n) = Sum_{k=1..n-1} k^2*sigma(k)*sigma(n-k).

Number of ways of placing n labeled balls into 3 indistinguishable boxes with at least 2 balls in each box.

Number of 1-factorizations of K_{n,n}.

a(n) = floor(cos(n)).

Stirling numbers of the second kind, S(n,5).

Unsigned Stirling numbers of first kind s(n,5).

Associated Stirling numbers: second-order reciprocal Stirling numbers (Fekete) a(n) = [[n, 3]]. The number of 3-orbit permutations of an n-set with at least 2 elements in each orbit.

a(n) = round(cos(n)).

Number of partially labeled trees with n nodes (4 of which are labeled).

One half of the number of permutations of [n] such that the differences have 4 runs with the same signs.

Number of permutations of length n with exactly two valleys.

Generalized tangent numbers d_(n,3).

Card matching: Coefficients B[n,3] of t^3 in the reduced hit polynomial A[n,n,n](t).

Generalized Euler numbers c(4,n).

Number of bipartite partitions of n white objects and 5 black ones.

Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-6 places.

a(n) = floor(sin(n)).

Nearest integer to sin(n).

Nearest integer to sinh(n).

Restricted permutations.

S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind.

Eulerian numbers (Euler's triangle: column k=4 of A008292, column k=3 of A173018).

a(n) = Sum_{k=1..n-1} k^3*sigma(k)*sigma(n-k).

Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places.

a(n) = floor(cosh(n)).

Number of genus 0 rooted maps with 6 faces and n vertices.

a(n) = floor(tan(n)).

S2(j,2j+3) where S2(n,k) is a 2-associated Stirling number of the second kind.

Eulerian numbers (Euler's triangle: column k=5 of A008292, column k=4 of A173018).

One half of the number of permutations of [n] such that the differences have 5 runs with the same signs.

Number of permutations of [n] with exactly 3 increasing runs of length at least 2.

Generalized class numbers c_(n,3).

Size of second largest n-arc in PG(2,q), where q runs through the primes and prime powers >= 7.