Sequences

Denominator of n * n-th harmonic number.

Numerator of 1/n + 2/(n-1) + 3/(n-2) + ... + (n-1)/2 + n.

Degrees of polynomials involved in analysis of a binary-tree valued Markov chain depending on one parameter; each polynomial has a unique root in [ 0,1 ], which is a lower bound for the transition from positive recurrence to null recurrence.

Related to Clebsch-Gordan formulas.

Number of 1's when n is written in base -2.

Number of permutations of n elements containing a 2-cycle.

Number of permutations of n elements containing a 3-cycle.

c(i,j) is cost of evaluation of edit distance of two strings with lengths i and j, when you use recursion (every call has a unit cost, other computations are free); sequence gives c(n,n).

Numbers k such that Hofstadter Q-sequence Q(k) (A005185) satisfies Q(k) = k/2.

a(n) = n + (n+1)^2 + (n+2)^3.

a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.

a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4 + (n+4)^5.

a(0) = 1; for n > 0, a(n) = number of rings with n elements.

Number of independent vertex sets in the n-hypercube graph Q_n.

Numerator of n*(n+5)/((n+2)*(n+3)).

Denominator of n*(n+5)/((n+2)*(n+3)).

Maximal cardinality of 2-distance set in R^n.

Expansion of Molien series for 5-dimensional group G_3 acting on Jacobi polynomials of ternary self-dual codes.

Molien series for complex 8-dimensional group N_3 of order 2^(2.3+2), a central extension of an extraspecial 2-group.

Molien series for Gamma_3(2).

Molien series for Hecke group H_{3,4}.

Molien series for group Gamma_{3,0}(2).

Molien series for full 8 X 8 Siegel modular group H_3 of order 371589120.

Poincaré (or Molien) series for ring of Siegel modular forms of genus 3 (associated with full modular group Gamma_3).

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

Expansion of (1+x^19)/((1-x^2)*(1-x^4)^2*(1-x^6)).

a(n) = Product_{i=1..n} (4^i - 1).

Order of 2^n X 2^n unitary group H_n acting on Siegel modular forms.

Order of unitary 2^n X 2^n group H_{n,4} acting on Siegel modular forms.

Poincaré series [or Poincare series] for ring of modular forms of genus 2.

Numerator of Bernoulli number B_n.

Denominator of Bernoulli number B_n.

Numerators of poly-Bernoulli numbers B_n^(k) with k=2.

Denominators of poly-Bernoulli numbers B_n^(k) with k=2.

Numerators of poly-Bernoulli numbers B_n^(k) with k=3.

Denominators of poly-Bernoulli numbers B_n^(k) with k=3.

Numerators of poly-Bernoulli numbers B_n^(k) with k=4.

Denominators of poly-Bernoulli numbers B_n^(k) with k=4.

a(n) = 2*(3^n) - 2^n.

Poly-Bernoulli numbers B_n^(k) with k=-3.

Poly-Bernoulli numbers B_n^(k) with k=-4.

Values of Zagier's function J_1.

Values of Zagier's function J_1(k) as k runs through the numbers -1, 0, 3, 4, 7, 8, ... which are == -1 or 0 mod 4.

Zagier's function -J_1(4*n-1).

Zagier's function J_1(4*n).

Expansion of 1/(1-x^2)^2 (included only for completeness - the policy is always to omit the zeros from such sequences).

Expansion of (1+4*x)/(1-34*x+x^2).

a(n) = binomial(n+2, 2) + binomial(n+4, 5).

a(n) = binomial(n+2,2) + binomial(n+3,3) + binomial(n+4,4) + binomial(n+5,5).

a(n) = C(n+2, 2) + C(n+2, 3) + C(n+2, 4) + C(n+2, 5).