Sequences

Average theta series of odd unimodular lattices of dimension 9 (multiplied by 17).

Average theta series of odd unimodular lattices of dimension 10 (multiplied by 5).

Average theta series of odd unimodular lattices of dimension 11 (multiplied by 31).

Average theta series of odd unimodular lattices of dimension 13 (multiplied by 691).

Average theta series of odd unimodular lattices of dimension 14 (multiplied by 61).

Average theta series of odd unimodular lattices of dimension 15 (multiplied by 43).

Average theta series of odd unimodular lattices of dimension 16 (multiplied by 17).

Average theta series of odd unimodular lattices of dimension 17 (multiplied by 929569).

Average theta series of odd unimodular lattices of dimension 18 (multiplied by 1385).

Average theta series of odd unimodular lattices of dimension 19 (multiplied by 3202291).

Average theta series of odd unimodular lattices of dimension 20 (multiplied by 31).

Average theta series of odd unimodular lattices of dimension 21 (multiplied by 5412941).

Average theta series of odd unimodular lattices of dimension 22 (multiplied by 50521).

Average theta series of odd unimodular lattices of dimension 23 (multiplied by 53057489).

Average theta series of odd unimodular lattices of dimension 24 (multiplied by 691).

Expansion of 1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1) (inverse of Salem polynomial).

Composite connected numbers: composite numbers k such that g(k) < g(u) + g(v) holds for all relatively prime factorizations k=u*v, where g(x) = ceiling(log_2 x).

Eisenstein series E_12(q) (alternate convention E_6(q)), multiplied by 691.

Eisenstein series E_16(q) (alternate convention E_8(q)), multiplied by 3617.

Eisenstein series E_20(q) (alternate convention E_10(q)), multiplied by 174611.

Eisenstein series E_24(q) (alternate convention E_12(q)), multiplied by 236364091.

A discrete version of the Mangoldt function: if n is prime then ceiling(log(n)) else 0.

A discrete version of the Mangoldt function: if n is prime then round(log(n)) else 0.

A discrete version of the Mangoldt function: if n is prime then floor(log(n)) else 0.

a(n) = floor(log(prime(n))).

log( n-th prime) rounded to nearest integer.

Binary order of n: log_2(n) rounded up to next integer.

Expansion of square root of q times normalized Hauptmodul for Gamma(4) in powers of q^8.

McKay-Thompson series of class 16B for the Monster group.

Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^3.

McKay-Thompson series of class 8E for the Monster group.

Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^5.

Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^6.

Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^7.

Expansion of 16/lambda(z) in powers of nome q = exp(Pi*i*z).

a(n) = a(n-1)*b(n-2)+2, b() given by A029758.

Gessel-Stanley triangle read by rows: triangle of coefficients of polynomials arising in connection with enumeration of intransitive trees by number of nodes and number of right nodes.

a(n) = 1 + C(2*n,n) + C(3*n,n).

Number of nonisomorphic and nonantiisomorphic relations.

Number of self-converse groupoids.

Number of self-converse semigroups of order n.

Number of connected functions on n points with a loop of length 3.

Number of connected functions on n points with a loop of length 4.

a(n) = gcd(prime(n)+prime(n+1), prime(n+1)+prime(n+2)).

Number of rooted trees where root has degree 4.

Number of rooted trees with 2-colored leaves.

Number of rooted trees with 3-colored leaves.

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

Euler transform of 3 2 1 1 1 1 1 1...

Euler transform of 4 3 2 1 1 1 1 1 1 1 ...