Sequences

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

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

Expansion of (1+x^6)/((1-x)^2*(1-x^6)).

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

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

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

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

Expansion of (1+2*x^3+x^4)/((1-x^2)^2*(1-x^4)); Molien series for 3-dimensional representation of group 2x = [ 2+,4+ ] = CC_4 = C4.

Expansion of (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)).

Expansion of (1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)).

Expansion of (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)).

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

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

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

Expansion of (1+2*x^5+x^9)/((1-x)^2*(1-x^9)).

Triangle of coefficients from fractional iteration of e^x - 1.

Number of proper partitions of a set of n labeled elements.

Triangle read by rows: T(n,k) = number of closed meander systems of order n with k<=n components.

Smallest number a(n) formed from consecutive sequences of digits of Pi and satisfying a(n) > a(n-1); first 3 is omitted.

Discrete logarithm of n to the base 2 modulo 11.

Discrete logarithm of n to the base 2 modulo 13.

Discrete logarithm of n to the base 2 modulo 19.

Largest square dividing n.

Largest cube dividing n.

Largest 4th power dividing n.

Liouville's function lambda(n) = (-1)^k, where k is number of primes dividing n (counted with multiplicity).

a(n) = p*(p-1)/2 for p = prime(n).

a(n) = floor(n/8)*ceiling(n/8).

Numbers k such that the decimal expansion of 5^k contains no zeros.

Number of monotone self-dual Boolean functions of n variables that are inequivalent under the symmetric group.

Number of self-dual Boolean functions of n variables with transitive symmetry group.

Number of inequivalent self-dual Boolean functions of n variables with transitive symmetry group.

Squares of NSW numbers (A002315): x^2 such that x^2 - 2y^2 = -1 for some y.

Squares of sequence A001653: y^2 such that x^2 - 2*y^2 = -1 for some x.

Numbers k such that k+1 and k/2+1 are squares.

Hypotenuses of primitive Pythagorean triangles.

Numbers k such that sum of divisors of k^2 is a square.

Squares whose sum of divisors is a square.

Numbers n such that the sum of divisors of n^3 is a square.

Numbers n such that sum of divisors of n^2 is a cube.

Congruent to 0 or 1 mod 5.

Numbers n such that n^2 and n have same last 2 digits.

Numbers k such that k^2 and k have same last 3 digits.

Numbers that are congruent to {0, 1, 4} mod 5.

Triangle T(n,k), n>=1, read by rows, where T(n,k) is the number of lattice polygons with area n and perimeter 2*k.

Numbers n such that n^3 and n have same last 2 digits.

a(n) = floor(n/9)*ceiling(n/9).

Number of equilibrium configurations for n bodies, each with a radial force from the center, with an opposite force acting radially from center of configuration.

a(n) = Sum_{k=0..6} binomial(n,k).

a(n) = Sum_{k=0..7} binomial(n,k).