Sequences

a(n) = 3^n*n^(n-1).

Number of labeled trees with 3-colored nodes.

Product_{k>=1}1/(1 - x^k)^a(k) = 1 + 2x.

Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 3x.

Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 4x.

Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 5x.

Product_{k>=1} (1 + x^k)^a(k) = 1 + 2x.

Product_{k>=1}(1 + x^k)^a(k) = 1 + 3x.

Product_{k>=1} ((1 + x^k)^a(k)) = 1 + 4x.

Product_{k>=1} (1+x^k)^a(k) = 1 + 5x.

Shifts left under inverse Euler transform.

Shifts left under Euler transform.

Shifts left under Weigh transform.

Shifts left and changes sign under Weigh transform.

Number of rooted identity trees with 2-colored leaves.

Number of rooted identity trees with 3-colored leaves.

Number of rooted identity trees with 2-colored nodes.

Number of identity trees with 2-colored nodes.

Number of rooted identity trees with 3-colored nodes.

Number of identity trees with 3-colored nodes.

Number of rooted identity trees of height n. Sets of rank n.

Number of n-node rooted identity trees of height at most 3.

Number of n-node rooted identity trees of height at most 4.

Number of n-node rooted identity trees of height at most 5.

Number of n-node rooted identity trees of height at most 6.

Number of n-node rooted identity trees of height at most 7.

Number of n-node rooted identity trees of height at most 8.

Number of n-node rooted identity trees of height 4.

Number of n-node rooted identity trees of height 5.

Number of n-node rooted identity trees of height 6.

Number of n-node rooted identity trees of height 7.

Number of n-node rooted identity trees of height 8.

Number of nodes in largest rooted identity tree of height n.

Number of rooted graphs on n labeled nodes where the root has degree 2.

Number of rooted connected graphs on n labeled nodes where the root has degree 2.

Number of rooted graphs on n labeled nodes where the root has degree 3.

Number of rooted connected graphs on n labeled nodes where the root has degree 3.

Number of primes < n^3.

Numbers k such that k > first location of string of k in decimal expansion of Pi.

Numbers k such that k < first location of string of k in decimal expansion of Pi.

First location of palindrome a(n) in decimal expansion of Pi is palindromic.

Numbers k such that k is a substring of its base-2 representation.

Numbers k such that k is a substring of its base-3 representation.

Numbers n with property that n is a substring of its base 4 representation.

Numbers n with property that n is a substring of its base 5 representation.

Numbers k with the property that k is a substring of its base-6 representation.

Number of primes < n^2.

Number of prime pairs {p,q}, such that pq < n^2.

Divisible exactly by the square of a prime.

Numerator of frequency of integers with smallest divisor prime(n).