Sequences

Gaussian binomial coefficient [n, 5] for q = 2.

Gaussian binomial coefficient [ n,2 ] for q=5.

Gaussian binomial coefficient [ n,3 ] for q = 5.

Gaussian binomial coefficient [ n,4 ] for q = 5.

Gaussian binomial coefficient [ 2n,n ] for q=5.

Gaussian binomial coefficient [ n,n/2 ] for q=5.

Sum of Gaussian binomial coefficients [n,k] for q=2 and k=0..n.

Sum of Gaussian binomial coefficients [ n,k ] for q=3.

Sum of Gaussian binomial coefficients [ n,k ] for q=4.

Sum of Gaussian binomial coefficients [ n,k ] for q=5.

Sum of Gaussian binomial coefficients [ n,k ] for q=6.

Sum of Gaussian binomial coefficients [ n,k ] for q=7.

Sum of Gaussian binomial coefficients [ n,k ] for q=8.

Erroneous version of A000085.

a(n) = 3 + n/2 + 7*n^2/2.

a(n) = 2^(n*(n-1)/2).

Number of hierarchical models on n labeled factors or variables with linear terms forced. Also number of antichain covers of a labeled n-set.

a(n) = 2^n + n.

Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.

a(0), a(1), a(2), ... satisfy Sum_{k=0..n} a(k)*binomial(n,k) = 2^binomial(n,2), for n >= 0.

a(n) = a(n-1) + 3*a(n-2) for n > 1, a(0) = a(1) = 1.

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

Related to representations as sums of Fibonacci numbers.

Related to representations as sums of Fibonacci numbers.

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

T(n+2,2) from table A045912 of characteristic polynomial of negative Pascal matrix.

T(n+3,3) from table A045912 of characteristic polynomial of negative Pascal matrix.

a(n) = 1 + n/2 + 9*n^2/2.

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

n*a(n) = 2*(2*n-1)*a(n-1) + 4*(n-1)*a(n-2) with a(0) = 1.

Erroneous version of A003406.

Number of integer partitions of n whose smallest part is equal to the number of parts.

Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).

Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).

Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).

Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.

Sums of prime divisors of Ruth-Aaron numbers (A006145).

Reversion of Ramanujan numbers.

Number of 4 X n binary matrices up to row and column permutations.

Number of 3-tuples (p_1, p_2, p_3) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.

Number of 4-tuples (p_1, p_2, ..., p_4) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.

Number of 5-tuples (p_1, p_2, ..., p_5) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.

Exponential generating function x*exp(x/(1-x)).

E.g.f.: 1/(1-x*exp(x)).

Number of labeled ordered partitions of an n-set into odd parts.

Expansion of e.g.f.: 1/(2-x-exp(x)).

Number of ternary squarefree words of length n.

a(n+1) = (n-1)*a(n) + n*n!.

a(n) = a(a(n-3)) + a(n-a(n-3)).

a(n)=a(a(n-4))+a(n-a(n-4)).