Sequences

Number of partitions of an n-gon into (n-5) parts.

Central polygonal numbers: a(n) = n^2 - n + 1.

a(n) = Fibonacci(n) + n.

a(n) = 9*4^n.

Cullen numbers: a(n) = n*2^n + 1.

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

a(n) = 10*4^n.

a(n) = Sum_{k=0..n-1} binomial(2*n,2*k)*a(k)*a(n-k-1).

Wilson remainders: a(n) = ((p-1)!+1)/p mod p, where p = prime(n).

Palindromic pentagonal numbers.

Coefficient of x^p (p = n-th prime) in x * Product_{k>=1} (1-x^k)^2*(1-x^11k)^2.

Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime.

a(n) = smallest number m such that for all k > m, either k or k+1 has a prime factor > prime(n).

Numerators of coefficients in an asymptotic expansion of the confluent hypergeometric function F(1-b; 2; 4b).

Denominators of coefficients in an asymptotic expansion of the confluent hypergeometric function F(1-b; 2; 4b).

Number of equivalence classes with primitive period n of base 3 necklaces, where necklaces are equivalent under rotation and permutation of symbols.

Number of equivalence classes of base-3 necklaces of length n, where necklaces are considered equivalent under both rotations and permutations of the symbols.

Number of N-equivalence classes of self-dual threshold functions of exactly n variables.

N-equivalence classes of threshold functions of n or fewer variables.

Number of N-equivalence classes of threshold functions of exactly n variables.

Number of N-equivalence classes of self-dual threshold functions of n or fewer variables.

Numbers congruent to {2, 4, 8, 16} (mod 20).

2nd differences are periodic.

Narayana-Zidek-Capell numbers: a(n) = 1 for n <= 2. Otherwise a(2n) = 2a(2n-1), a(2n+1) = 2a(2n) - a(n).

Sinh(x) / cos(x) = Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)!.

From the expansion of sinh(x) / cos(x): a(n) = odd part of A002084(n).

Number of circulant tournaments on 2n+1 nodes up to Cayley isomorphism.

Number of point-symmetric tournaments with 2n+1 nodes.

Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010.

a(n) = 11*4^n.

Related to Hamilton numbers.

From a Goldbach conjecture: the location of records in A185091.

From a Goldbach conjecture: records in A185091.

Highly abundant numbers: numbers k such that sigma(k) > sigma(m) for all m < k.

Number of unlabeled connected loop-less graphs on n nodes containing exactly one cycle (of length at least 2) and with all nodes of degree <= 4.

Number of partitions of n into nonprime parts.

Mixed partitions of n.

Numbers that are not the sum of 3 nonzero triangular numbers.

G.f.: 1/Product_{k>=1} (1-prime(k)*x^prime(k)).

G.f.: -1 + Product_{k>=1} (1 + prime(k)*x^prime(k)).

a(n) = number of partitions of n into semiprimes (more precisely, number of ways of writing n as a sum of products of 2 distinct primes).

Nearest integer to 4 * Pi * n^3 / 3.

Number of nonnegative solutions to x^2 + y^2 + z^2 = n.

Coefficients of expansion of Jacobi nome q in certain powers of (1/2)*(1 - sqrt(k')) / (1 + sqrt(k')).

Logarithmic numbers.

Reduced tangent numbers: 2^n*(2^{2n} - 1)*|B_{2n}|/n, where B_n = Bernoulli numbers.

Number of transitive permutation groups of degree n.

Expansion of Product_{k>=1} (1 - x^k)^2.

4th powers written backwards.

Hyperfactorials: Product_{k = 1..n} k^k.