Sequences

Coefficients of modular function G_2(tau).

Coefficients of modular function G_3(tau).

Coefficients of modular function G_4(tau).

Exponents m_i associated with Weyl group W(E7).

Coefficients of modular function denoted G_6(tau) by Atkin.

Size of Doehlert-Klee design with n blocks.

a(n) = cost of minimal multiplication-cost addition chain for n.

Solutions k to k^2 = a^2 + b^2 + c^2 (a,b,c > 0).

Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the left of the rightmost top vertex.

Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the right of the rightmost top vertex.

Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex and rightmost top vertex have the same x-coordinate.

Number of n-covers of an unlabeled 5-set.

Number of permutations of length n with 2 cycle lengths.

Number of directed animals of size n (or directed n-ominoes in standard position).

Number of directed animals of size n (k=1 column of A038622); number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, where s(0) = 2; also sum of row n+1 of array T in A026323.

Number of compact-rooted directed animals of size n having 3 source points.

Exponents m_i associated with Weyl group W(E_8).

Rook polynomials.

Rook polynomials.

a(n) = largest integer such that every tournament on n nodes contains a consistent set of n arcs.

Erroneous version of A033678.

Erroneous version of A273867.

Number of n-gons in cubic curve.

Number of 3-covers of an unlabeled n-set.

Number of 4-covers of an unlabeled n-set.

Number of 5-covers of an unlabeled n-set.

Number of 6-covers of an unlabeled n-set.

Reachable configurations on n circles.

Conductors of elliptic curves.

3-dimensional Catalan numbers.

4-dimensional Catalan numbers.

5-dimensional Catalan numbers.

Positive numbers that are the sum of 2 squares or 3 times a square.

Number of O_1^{2+}(Z)-orbits of Lorentzian modular group.

Number of SO_1^{2+}(Z) orbits of Lorentzian modular group.

Degrees of fundamental invariants of Weyl group W(E_7).

Degrees of fundamental invariants of Weyl group W(E_8).

Expansion of Jacobi nome q in terms of parameter m/16.

Expansion of (theta_2(q)/theta_3(q))^4/16 in powers of q.

Generalized Euler numbers of type 2^n.

Generalized Euler numbers of type 3^2n.

Generalized tangent numbers of type 3^(2n+1).

Number of permutations in S_n with longest increasing subsequence of length <= 3 (i.e., 1234-avoiding permutations); vexillary permutations (i.e., 2143-avoiding).

Second-order Eulerian numbers: a(n) = 2^n - 2*n.

Number of phylogenetic rooted trees with n labels.

Number of phylogenetic trees with n labels.

Number of comparative probability orderings on n elements.

Sum of adjacent Catalan numbers.

Numbers k such that (11^k - 1)/10 is prime.

a(n) = binomial(3n,n).