Sequences

Odd numbers k such that {1..k-1} can be partitioned into disjoint sets I, J with 2I == -J (mod k) such that I, J are unions of cyclotomic cosets mod k.

Odd numbers k such that {1..k-1} cannot be partitioned into disjoint sets I, J such that 2I == -J (mod k) and I, J are unions of cyclotomic cosets mod k.

Elements in the 5-Pascal triangle (by row).

Elements in the 5-Pascal triangle A028313 that are not 1.

Odd elements in the 5-Pascal triangle A028313.

Odd elements in the 5-Pascal triangle A028313 that are not 1.

Even elements in the 5-Pascal triangle A028313.

Distinct elements in the 5-Pascal triangle A028313.

Distinct odd elements in the 5-Pascal triangle A028313.

Distinct even elements in the 5-Pascal triangle A028313.

Even elements to the right of the central elements of the 5-Pascal triangle A028313.

Central elements in the 5-Pascal triangle A028313.

Elements to the right of the central elements of the 5-Pascal triangle A028313.

Elements to the right of the central elements of the 5-Pascal triangle A028313 that are not 1.

Odd elements to the right of the central elements of the 5-Pascal triangle A028313.

Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k).

Elements in the even-Pascal triangle A028326 that are not 2.

Distinct elements in the even-Pascal triangle A028326.

Twice central binomial coefficients.

Elements to the right of the central elements of the even-Pascal triangle A028326.

Elements to the right of the central elements of the even-Pascal triangle A028326 that are not 2.

Distinct elements to the right of the central elements of the even-Pascal triangle A028326.

Number of nonzero terms in expansion of square of Vandermonde determinant of order (n+1)x(n+1) in terms of Schur functions.

Differences between consecutive odd primes, divided by 2.

Number of decimal digits in n-th Mersenne prime.

Positive numbers k such that k*(k+1) is a palindrome.

Palindromes of the form k*(k + 1).

Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x.

Coefficient of x^2 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

Coefficient of x^3 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

Coefficient of x^4 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

Expansion of Product_{i>=1} (1 - x^i)^(-1/i); also of exp(Sum_{n>=1} (d(n)*x^n/n)) where d is number of divisors function.

Expansion of Product_{i>=1} (1-x^i)^(1/i); also of exp(- Sum_{n>=1}(d(n)*x^n/n)) where d(n) is the number of divisors of n.

Molien series for complete weight enumerator of self-dual code over GF(5).

Molien series for complete weight enumerator of self-dual code over GF(5) containing all-1's vector.

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

a(n) = n^2 - 4.

Numbers k such that k^2 + 3*k + 1 is a palindrome.

Palindromes of form n^2 + 3*n + 1.

Expansion of -1/x + 6*3F2( 5/6, 1, 7/6; 3/2, 2; 108*x).

Dimension of invariant subspace of Lie polynomials of degree 2n under action of SL_2(C) on free Lie algebra of rank 2.

A Golomb-like recurrence that decreases infinitely often.

Coefficient of x^(2*n+1) in arctanh(x)/sqrt(1-x^2), multiplied by (2*n+1)!.

How the astronomical clock ("Orloj") in Prague strikes the hours (digits follow 12343212343... (A028356), n-th group adds to n).

How the astronomical clock ("Orloj") in Prague would strike 1,2,3,...,24,25,.. (digits follow 12343212343... (A028356), n-th group adds to n).

Simple periodic sequence underlying clock sequence A028354.

Partial sums of A028356.

Partial sums of A028357.

Two-bell analog of A028355.

Continued fraction for (e + 1)/3.