Sequences

a(n) = Sum_{k = 0..n} binomial(n,k)^4.

a(n) = Sum_{k = 0..n} C(n,k)^5.

a(n) = floor((7*2^(n+1)-9*n-10)/3).

Number of labeled Greg trees.

Number of labeled rooted Greg trees with n nodes.

a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the smallest prime factor of b(n)-1.

a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the largest prime factor of (b(n)-1).

a(n) = -1 + a(0)*a(1)*...*a(n-1) with a(0) = 3.

Number of elementary sequences of length n.

a(n) = number of length-n sequences s with s[1]=1, s[2]=1, s[k-1] <=s[k] <= s[k-2]+s[k-1] (s is called a sub-Fibonacci sequence of length n).

Number of sequences s of length n with s[1]=1, s[2]=1, s[j-1]<s[j]<=s[j-2]+s[j-1] for j>=3.

Number of perfect matchings in n-cube.

Number of Van Lier sequences of length n.

(5,4)-graphs.

(6,5)-graphs.

(7,6)-graphs.

Betrothed (or quasi-amicable) numbers.

Nontotients: even numbers k such that phi(m) = k has no solution.

Noncototients: numbers k such that x - phi(x) = k has no solution.

Numbers having divisors d, e with d < e < 2*d.

Davenport-Schinzel numbers of degree 5 on n symbols.

Davenport-Schinzel numbers of degree 6 on n symbols.

Mian-Chowla sequence (a B_2 sequence): a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all distinct.

Number of permutations of (1,...,n) having n-5 inversions (n>=5).

Number of permutations of (1,...,n) having n-6 inversions (n>=6).

Number of permutations of (1,...,n) having n-7 inversions (n>=7).

a(n) = (n + 3)*(n^2 + 6*n + 2)/6.

Number of permutations of [n] with four inversions.

a(n) = C(n,5) + C(n,4) - C(n,3) + 1, n >= 7.

Number of graphs on n nodes with 3 cliques.

Representation degeneracies for boson strings.

Representation degeneracies for boson strings.

Representation degeneracies for boson strings.

Representation degeneracies for boson strings.

Representation degeneracies for boson strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Neveu-Schwarz strings.

Representation degeneracies for Ramond strings.

Representation degeneracies for Ramond strings.

Representation degeneracies for Ramond strings.

Representation degeneracies for Ramond strings.

Bosonic string states.

Bosonic string states.

Fermionic string states.