Sequences

Numerators of Taylor series for 1/(sin x + tan x).

Number of letters in n (in Polish), excluding spaces and hyphens.

Initial digit of Fibonacci number F(n).

Number of elements of order <= 2 in group of n X n upper triangular matrices over GF(2).

Number of necklaces of sets of beads containing a total of n beads.

a(n) = 1 if n is squarefree, otherwise 0.

Coefficients of Gaussian polynomials q_binomial(n-2, 2). Also triangle of distribution of rank sums: Wilcoxon's statistic. Irregular triangle read by rows.

Triangle of distribution of rank sums: Wilcoxon's statistic.

Triangle read by rows of differences of reciprocals of unity.

Triangle T(n,k) = P(n,k)/2, n >= 2, 1 <= k < n, of one-half of number of permutations of 1..n such that the differences have k runs with the same signs.

Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of length at least 2.

n^2 raised to power n^2.

Fibonacci number F(n) to power F(n).

Triangular number t(n) raised to power t(n).

Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 10.

Orders of non-cyclic simple groups (divided by 4).

a(n) = (4*n)!/(n!)^4.

a(n) = (5*n)!/(n!)^5.

a(n) = (6n)!/(n!)^6.

Number of immersions of the oriented circle into the oriented plane with n double points.

Number of immersions of the unoriented circle into the oriented plane with n double points.

Number of immersions of the oriented circle into the unoriented plane with n double points.

Number of immersions of the unoriented circle into the unoriented plane with n double points.

Number of immersions of the oriented circle into the oriented plane with n double points and index n-1.

Triangle T(n,k) giving number of immersions of the oriented circle into the oriented plane with n double points and index k, k = -n-1, -n+1, ..., n-1, n+1.

Number of immersions of oriented circle into oriented sphere with n double points.

Number of immersions of an unoriented circle into the oriented sphere with n double points.

Number of immersions of oriented circle into unoriented sphere with n double points.

Number of immersions of an unoriented circle into the unoriented sphere with n double points.

Numerators of sequence having sqrt(cos(x)) as e.g.f. (even-indexed coefficients only).

Numerators of coefficients in expansion of sqrt(sin(x)/x) (even powers only).

Denominators of coefficients in expansion of sqrt(sin(x)/x) (even powers only).

Numerators of coefficients in expansion of cube root of sin(x).

Denominators of coefficients in expansion of cube root of sin(x).

Increasing length runs of consecutive composite numbers (endpoints).

Increasing length runs of consecutive composite numbers (records).

Orchard problem with 5 trees in a row (may not have all been proved optimal).

a(n) = 2*a(n-1) + a(n-3), with a(0)=1 and a(1)=2.

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

Ordered hypotenuse numbers (squares are sums of 2 distinct nonzero squares).

Expansion of e.g.f: (1+x)*cos(x).

Expansion of (1+x)/cos(x).

Hypotenuse numbers (squares are sums of 2 nonzero squares).

Ordered short legs of Pythagorean triangles.

All natural numbers except 1, 2 and 4.

Expansion of e.g.f.: 1 + tan(x).

Expansion of 1/cos(log(1+x)).

Expansion of e.g.f.: 1/cos(sin(x)) (even-indexed coefficients only).

Expansion of e.g.f.: 1/cos(sinh(x)) (even-indexed coefficients only).

Expansion of e.g.f.: 1/cos(tan(x)) (even-indexed coefficients only).