Sequences

Expansion of (1+x^18)/((1-x)*(1-x^2)*(1-x^3)).

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

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

Number of 3 X 3 symmetric stochastic matrices under row and column permutations.

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

Expansion of (1+x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

a(n) = floor(n/7)*ceiling(n/7).

Expansion of (1+x^7)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Theta series of (probably nonexistent) exceptionally good 16-dimensional sphere packing.

Expansion of e.g.f. 2/(1 + cos x * cosh x) in powers of x^4.

Pisot sequences E(2,6), L(2,6), P(2,6), T(2,6).

Number of dots and dashes used when representing n-th letter in Morse code.

a(n) = (n+1)*(n^2 +8*n +6)/6. Number of n-dimensional partitions of 4. Number of terms in 4th derivative of a function composed with itself n times.

Number of n-dimensional partitions of 5.

a(n) = (n-dimensional partitions of 6) + C(n,4) + C(n,3).

For any circular arrangement of 0..n-1, let S be the sum of cubes of every sum of two contiguous numbers; then a(n) is the number of distinct values of S.

For any circular arrangement of 0..n-1, let S = sum of squares of every sum of three contiguous numbers; then a(n) = # of distinct values of S.

Period of continued fraction representation of (sqrt(4n+1)+1)/2=sqrt(n+sqrt(n+sqrt(n+...))).

Numbers k such that sqrt(-1) mod k exists; or, numbers that are primitively represented by x^2 + y^2.

a(n) = (n+4)^n.

a(n) = (n+5)^n.

a(n) = (n + 6)^n.

a(n) = n^(n+2).

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

a(n) = n^(n+4).

a(n) = n^(n+5).

Amino acid numbers, based on the rules made to assign each amino acid a unique number smaller than 64.

The problem of the calissons: number of ways to tile a hexagon of edge n with diamonds of side 1. Also number of plane partitions whose Young diagrams fit inside an n X n X n box.

Squares repeated; a(n) = floor(n/2)^2.

Molien series for 3-dimensional representation of dihedral group D_6 of order 6.

Molien series for 3-dimensional group [2,3]+ = 223; also for group H_{1,2} of order 384.

Molien series for group [2,4]+ = 224.

Molien series for group [2,5]+ = 225.

Molien series for group [2,6]+ = 226.

Molien series for group [2,7]+ = 227.

Molien series for group [2,8]+ = 228.

Molien series for group [2,9]+ = 229.

Molien series for group [2,10]+ = 2 2 10.

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

Triangular numbers repeated.

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

Expansion of (1+x^5)/((1-x^2)^2*(1-x^5)).

Expansion of (1+x^7)/((1-x^2)^2*(1-x^7)).

Expansion of (1+x^9)/((1-x^2)^2*(1-x^9)).

a(n) = ceiling(n^2/3).