Sequences

Number of labeled servers of dimension 24.

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

If n is an odd prime, a(n) = the number of primitive roots mod n, otherwise a(n) = the number of k < n divisible by at least one but not all of the prime factors of n.

G.f. for Moebius transform is x * (1 + x) / (1 + x^4).

Number of rooted unlabeled trees on n nodes having a primary branch.

Number of unlabeled (and unrooted) trees on n nodes having a centroid.

Number of distinct products i*j with 0 <= i, j <= 2^n - 1.

Duplicate of A035508.

Number of distinct products i*j with 0 <= i, j <= n-th prime.

Triangle T00, T10, T01, T20, T11, T02, etc., where Tmn = number of distinct products ij with min(m,n) <= i,j <= max(m,n).

Triangle T(n,k) = number of distinct products i*j with k<=i,j<=n, for 0<=k<=n.

Triangle T00, T10, T11, T20, T21, T22, etc. where Tmn = number of distinct products ij with m-n<=i,j<=m.

Number of divisors of n!.

Number of distinct products ij with 1 <= i, j <= n (number of distinct terms in n X n multiplication table).

Number of distinct products ijk with 1 <= i,j,k <= n.

Number of distinct products ijk with 0 <= i,j,k <= n.

Number of distinct products ij with 0 <= i < j <= n.

Number of distinct products ij with 1 <= i < j <= n. (Number of terms appearing more than once in a 1-to-n multiplication table.)

Number of distinct products ijk with 0 <= i < j < k <= n.

Number of distinct products i*j*k with 1 <= i < j < k <= n.

Continued fraction for Pi^3/zeta(3).

Related to sorting procedure studied by West: number of permutations that are both sorted (i.e., obtainable as output of the sorting procedure) and one-stack sortable.

Sum over all 2^(2n) pairs (u,v) of binary sequences of length n of length of maximal common subsequence between them.

a(1) = 2; then defined by property that a(n) = smallest number >= a(n-1) such that successive runs have lengths 1,1,2,2,3,3,4,4.

Number of distinct products ij with 1 <= i <= n, 1 <= j <= n, (i,j)=1.

G.f. f(x) = Sum_{n>=1} a(n)*x^n satisfies f(f(x)) = x*(1 + 4*x).

a(n) = floor( e * 2^n ).

Largest prime factor of [e*2^n].

Expansion of 1/(1 - 4*x + 5*x^2 - 3*x^3).

TV channels in Tokyo.

a(n) = (n^4 + n)/2 (Row sums of an n X n X n magic cube, when it exists).

For n odd, >1, not divisible by 3, we can write 3/n = 1/a + 1/b + 1/c with a>b>c>0, a,b,c distinct and odd; sequence gives smallest a.

For n != 1 mod 3, we can write 3/(2n+1) = 1/a + 1/b + 1/c with a>b>c>0, a,b,c distinct and odd; sequence gives smallest such a, or 1 if n = 1 mod 3.

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

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

Triangle read by rows: square of the lower triangular mean matrix.

Triangle read by rows: cube of the lower triangular mean matrix.

Triangle read by rows: 4th power of the lower triangular mean matrix (M[i,j] = 1/i for i <= j).

Second diagonal of A027446.

Third diagonal of A027446.

First diagonal of A027447.

Second diagonal of A027447.

Third diagonal of A027447.

First diagonal of A027448.

Second diagonal of A027448.

Third diagonal of A027448.

a(n) = (H(n) - 1)*lcm{1,...,n}, where H(n) is the n-th harmonic number.

Third column of A027446.

Numerator of Sum_{k=1..n} H(k)/k, where H(k) is k-th harmonic number.

Second column of A027447.