Sequences

23rd powers: a(n) = n^23.

24th powers: a(n) = n^24.

25th powers: a(n) = n^25.

Perimeters of integer-sided right triangles.

From Euler's Pentagonal Theorem: coefficient of q^n in Product_{m>=1} (1 - q^m).

Expansion of Product_{k>=1} (1 - x^k)^3.

Expansion of Product_{k>=1} (1 - x^k)^9.

Expansion of Product (1 - x^k)^10 in powers of x.

Expansion of Product_{k>=1} (1 - x^k)^11.

Expansion of Product_{k>=1} (1 - x^k)^13.

Expansion of Product_{k>=1} (1 - x^k)^14.

Expansion of Product_{k>=1} (1 - x^k)^15.

Expansion of Product_{k>=1} (1 - x^k)^17.

Expansion of Product_{k>=1} (1 - x^k)^18.

Expansion of Product_{k>=1} (1 - x^k)^19.

Expansion of Product_{k>=1} (1 - x^k)^20.

Expansion of Product_{k>=1} (1 - x^k)^21.

Expansion of Product_{k>=1} (1 - x^k)^22.

Expansion of Product_{k>=1} (1 - x^k)^23.

Expansion of Product_{k>=1} (1-x^k)^25.

Expansion of Product_{k>=1} (1-x^k)^26.

Expansion of Product_{k>=1} (1-x^k)^27.

Expansion of Product_{k>=1} (1-x^k)^28.

Expansion of Product_{k>=1} (1-x^k)^29.

Expansion of Product_{k>=1} (1-x^k)^30.

Expansion of Product_{k>=1} (1-x^k)^31.

Expansion of Product_{k>=1} (1-x^k)^32.

Expansion of Product_{k>=1} (1-x^k)^44.

Expansion of Product_{k >= 1} (1-x^k)^48.

Expansion of Product_{k>=1} (1-x^k)^40.

Expansion of Product_{k>=1} (1-x^k)^64.

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

Incomplete Gamma Function at -3.

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

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

Number of numbers <= n whose set of prime factors is a subset of the set of prime factors of n.

Number of numbers <= n with a prime factor that does not divide n.

Number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.

Let S(x,y) = number of lattice paths from (0,0) to (x,y) that use the step set { (0,1), (1,0), (2,0), (3,0), ....} and never pass below y = x. Sequence gives S(n-3,n).

Constant sequence: a(n) = 11.

Constant sequence: a(n) = 12.

Constant sequence: a(n) = 13.

Constant sequence: a(n) = 14.

Constant sequence: a(n) = 15.

Constant sequence: a(n) = 16.

Constant sequence: a(n) = 17.

Constant sequence: a(n) = 18.

Constant sequence: a(n) = 19.

Constant sequence: a(n) = 20.

Constant sequence: a(n) = 21.