Sequences

Numbers whose total number of prime factors (counting multiplicity) is squarefree.

Elements in 3-Pascal triangle (by row).

Elements in 3-Pascal triangle A028262 (by row) that are not 1.

Odd elements in 3-Pascal triangle A028262 (by row).

Odd elements in 3-Pascal triangle A028262 (by row) that are not 1.

Even elements in 3-Pascal triangle A028262 (by row).

Number of distinct elements in 3-Pascal triangle A028262 (by row).

Distinct odd elements in 3-Pascal triangle A028262 (by row).

Distinct even elements in 3-Pascal triangle A028262 (by row).

Central elements in 3-Pascal triangle A028262 (by row).

Elements to right of central elements in 3-Pascal triangle A028262.

Elements to right of central elements in 3-Pascal triangle A028262 that are not 1.

Even elements to right of central elements in 3-Pascal triangle A028262.

Odd elements (greater than 1) to right of central elements in 3-Pascal triangle A028262.

Elements in 4-Pascal triangle (by row).

Elements in 4-Pascal triangle A028275 (by row) that are not 1.

Odd elements in 4-Pascal triangle A028275 (by row).

Odd elements in 4-Pascal triangle A028275 (by row) that are not 1.

Even elements in 4-Pascal triangle A028275 (by row).

Distinct elements in 4-Pascal triangle A028275 (by row).

Distinct odd elements in 4-Pascal triangle A028275 (by row).

Distinct even elements in 4-Pascal triangle A028275 (by row).

Central elements in 4-Pascal triangle A028275 (by row).

Elements to right of central elements in 4-Pascal triangle A028275.

Elements to right of central elements in 4-Pascal triangle A028275 that are not 1.

Even elements to right of central elements in 4-Pascal triangle A028275.

Odd elements (greater than 1) to right of central elements in 4-Pascal triangle A028275.

Molien series for complex 4-dimensional Clifford group of order 92160 and genus 2. Also Molien series of ring of biweight enumerators of Type II self-dual binary codes.

Expansion of (1+x^2+x^3+x^5)/((1-x)(1-x^3)(1-x^4)(1-x^6)).

Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)).

Expansion of 1/((1-x)^2(1-x^2)(1-x^3)(1-x^5)) in powers of x.

Numbers of letters in n (in the Norwegian language Nynorsk).

Period 7.

a(n) = n^5 - (65/6)*n^4 + (173/6)*n^3 + (148/3)*n^2 - (862/3)*n + 265.

a(n) = n^6 - (883/60)*n^5 + (157/3)*n^4 + (2155/12)*n^3 - (4570/3)*n^2 + (42767/15)*n - 967.

Expansion of e.g.f. Gudermannian(x) = 2*arctan(exp(x)) - Pi/2.

Coefficients of Chebyshev polynomials of the first kind: triangle of coefficients in expansion of cos(n*x) in descending powers of cos(x).

Triangle of coefficients in expansion of sin(n*x) (or sin(n*x)/cos(x) if n is even) in ascending powers of sin(x).

Weight distribution of the dodecacode, a [[12,0,6]] quantum-error-correcting code.

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

a(n) = a(n-1)^2 + prime(n-1), with a(1) = 1.

a(n) = prime(n)*Catalan(n).

a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.

Triangle read by rows of numbers of permutations eliminating just card k out of n in game of Mousetrap.

Form a triangle with n numbers in top row; all other numbers are the sum of their parents. E.g.: 4 1 2 7; 5 3 9; 8 12; 20. The numbers must be positive and distinct and the final number is to be minimized. Sequence gives final number.

Form a triangle with n numbers in top row; all other numbers are the product of their parents. The numbers must be positive and distinct and the final number is to be minimized.

Molien series for ring of symmetrized weight enumerators of self-dual codes (with respect to Euclidean inner product) of length n over GF(4).

Expansion of (1 - x + x^2) / (1 - x)^2 in powers of x.