Sequences

a(n) = 3*(n+1)*binomial(n+5,6).

a(n) = 7*(n+1)*binomial(n+5,7).

a(n) = 14*(n+1)*binomial(n+5,8).

a(n) = 126*(n+1)*binomial(n+5,9)/5.

a(n) = 42*(n+1) * binomial(n+5,10).

a(n) = 66*(n+1)*binomial(n+5,11).

a(n) = 99*(n+1)*binomial(n+5,12).

a(n) = (n+1)*binomial(n+6,6).

a(n) = 7*(n+1)*binomial(n+6,7)/2.

a(n) = 28*(n+1)*binomial(n+6,8)/3.

a(n) = 21*(n+1)*binomial(n+6,9).

a(n) = 42*(n+1)*binomial(n+6,10).

a(n) = 77*(n+1)*binomial(n+6,11).

If there were a unimodular 25-dimensional lattice with minimal norm 3, it would have this as its theta series. Unfortunately, no such lattice exists.

If there were a unimodular 25-dimensional lattice with minimal norm 3, it would have this as the theta series of its shadow. Unfortunately, no such lattice exists.

Inverse binomial transform of a_0 = 1, a_1, a_2, etc. is a_0, 0, a_1, 0, a_2, 0, etc.

Values of k for which 11 divides A000041(k).

First differences of A010785.

Palindromic squares with an even number of digits.

Numbers k such that k + (k+1)^2 + (k+2)^3 + (k+3)^4 + (k+4)^5 is prime.

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

Number of symmetric {-1, +1} matrices of order n with nonnegative row and column sums.

Distances between successive 2's in sequence A001223 of differences between consecutive primes.

Number of labeled strongly connected n-state 2-input automata.

Number of unlabeled strongly connected n-state 2-input automata.

Total number of vertices in all loopless rooted planar maps with n edges.

Number of subgroups of index n in free group of rank 3.

Number of subgroups of index n in fundamental group of a certain fiber space.

Number of subgroups of index n in fundamental group of a certain fiber space.

Number of subgroups of index n in fundamental group of a certain fiber space.

Number of subgroups of index n in fundamental group of a certain fiber space.

Number of subgroups of index n in fundamental group of a certain fiber space.

Duplicate of A027840.

Number of subgroups of index n of fundamental group of the non-orientable cycle bundle over the Klein bottle.

Number of subgroups of index n in fundamental group of a certain fiber space.

Number of subgroups of index n in fundamental group of a certain fiber space.

a(n) = Sum_{d|n} sigma(n/d)*d^3.

a(n) = Sum_{ d|n } sigma(n/d)*d^4.

a(n) = (n+1)*(5*n^2+4*n+1).

a(n) = (n+1)*(14*n^3+13*n^2+6*n+1).

Number of nonisomorphic semigroups of order n.

Number of connected functions on n points with a loop of length 2.

Functions on n points with a single labeled point.

Mutinous numbers: n > 1 such that n/p^k > p, where p is the largest prime dividing n and p^k is the highest power of p dividing n.

Antimutinous numbers: n>1 such that n/p^k < p, where p is the largest prime dividing n and p^k is the highest power of p dividing n.

Dan numbers: numbers m of the form 2^j * 3^k such that m +- 1 are twin primes.

Number of positive divisors of n!, read mod n.

Triangle of "Harmonic Coefficients" T(n,k), read by rows: (Sum_{i=1..n} T(n,i) * k^i) * k! / ((n+k)! * n!) = (Sum_{i=1..k} (1/i-1/(i+n)) = n * (Sum_{i=1..k} 1/(i*(i+n)))).

Theta series of odd Leech lattice (the unique unimodular 24-dimensional lattice with minimal norm 3).

a(n) = (-tau(n) + sigma_11(n)) / 691, where tau is Ramanujan's tau (A000594), sigma_11(n) = Sum_{ d divides n } d^11 (A013959).