Sequences

Expansion of a modular function for Gamma_0(15).

Expansion of a modular function for Gamma_0(21).

Expansion of chi(x)^10 / phi(x)^4 in powers of x where phi(), chi() are Ramanujan theta functions.

Number of "cubic partitions" of n: expansion of Product_{k>0} 1/((1-x^(2k))^2*(1-x^(2k-1))) in powers of x.

Coefficients in the asymptotic expansions of modified Hankel functions h_1(z) and h_2(z), rounded to nearest integer.

Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.

Earliest sequence with a(a(n)) = 2n.

Earliest sequence with a(a(n))=3n.

Earliest sequence with a(a(n))=5n.

Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.

Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.

Weight distribution of [ 28,14,9 ] ternary self-dual code.

a(n) = n^2 + 1.

a(n) = n^4 + 1.

Number of permutations of length n within distance 2 of a fixed permutation.

Number of permutations according to distance.

Number of permutations of length n within distance 3 of a fixed permutation.

Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 3.

a(n) = A188491(n+1) - A188494(n) - A002526(n).

a(n) = A002527(n+1) - A002527(n) - A002526(n).

a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.

a(2*n) = a(2*n-1) + a(2*n-2), a(2*n+1) = 2*a(2*n) + a(2*n-1); a(0) = a(1) = 1.

a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 0, a(1) = 1.

a(n) = 2*a(n-1) + 5*a(n-2), with a(0) = a(1) = 1.

a(n) = 2*a(n-1) + 9*a(n-2), with a(0) = 0, a(1) = 1.

a(n) = 2*a(n-1) + 9*a(n-2), with a(0)=a(1)=1.

a(n) = 8*a(n-2) - 9*a(n-4).

a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).

Second-order Eulerian numbers <<n+1,n-1>>.

Eulerian numbers of the second kind: <<n+3, n>>.

Increasing gaps between prime-powers.

a(n) = Sum_{k=1..n-1} floor((n-k)/k).

Number of two-valued complete Post functions of n variables.

Complete Post functions of n variables.

a(n) = binomial(2*n+1,n)*(n+1)^2.

Numerator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).

Denominator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).

Numerator of the n-th harmonic number H(n) divided by (n+1); a(n) = A001008(n) / ((n+1)*A002805(n)).

Denominators of coefficients for numerical differentiation.

Numerators of coefficients of log(1+x)/sqrt(1+x).

Denominators of coefficients of log(1+x)/sqrt(1+x).

Numerators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).

Denominators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).

Coefficients for numerical differentiation.

Numerators of coefficients for numerical differentiation.

Denominators of coefficients for numerical differentiation.

Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.

Odd squarefree numbers with an even number of prime factors that have no prime factors greater than 31.

Coefficients of a Dirichlet series.

Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.