Sequences

Values of A038007 ending in 2.

Differences of A038011.

Values of A038005 ending in 3.

Differences of A038013.

Number of pointed (distinguished element) idempotent groupoids.

Number of pointed (distinguished element) commutative groupoids.

Number of n-element commutative groupoids with an identity ("pointed" groupoids).

Triangle read by rows: T(n,k) is the number of groupoids with n elements and k idempotents.

Triangle: T(n,k), k<=n: groupoids with no symmetry with n elements and k idempotents.

Triangle: T(n,k), k<=n: groupoids with a nontrivial symmetry with n elements and k idempotents.

Triangle read by rows: T(n,k) is the number of commutative groupoids with n elements and k idempotents.

Triangle: T(n,k), k<=n: commutative groupoids with no symmetry with n elements and k idempotents.

Triangle: T(n,k), k<=n: commutative groupoids with a nontrivial symmetry with n elements and k idempotents.

Number of k's such that A002034(k) = n.

Winner of n-th Littlewood Frog Race.

Last position reached by winner of n-th Littlewood Frog Race.

Least k such that A038025(k)=n-th composite number or 0 if none.

Position reached by frog in A038027 or 0 if none. A038026(A038027(n)).

Incrementally largest values of A038025.

Indices of incrementally largest values of A038025.

Position reached by frog in A038029. A038026(A038029(n)).

A038025(n)=1.

a(n) = A000166(n-1)*n*(n-1).

Number of compositions (ordered partitions) of 1 into {1/1, 1/2, 1/3, ..., 1/n}.

Number of labeled dyslexic planted planar trees with n+1 nodes.

Number of nonisomorphic and nonantiisomorphic rings with n elements.

Number of labeled rooted compound windmills (mobiles) with n nodes.

Number of labeled dyslexic rooted compound windmills with n nodes.

a(n) = Sum_{d|n} (2^d*3^(n/d)).

a(n) = n*d(n), where d(n) = number of divisors of n (A000005).

Number of ways to partition an n-set into subsets of equal size.

Number of ways to partition a 2-colored labeled set into identical subsets.

Number of ways to partition a labeled set into 2-colored subsets of equal size.

Shifts left under transform T where Ta is a DCONV a.

Shifts left under transform T where Ta is phi DCONV a.

Shifts left under transform T where Ta is (identity) DCONV a.

Shifts left under transform T where Ta is a EXP-DCONV a.

a(n) = (n-1)! * sigma(n).

Number of labeled rooted trees with 2-colored leaves.

Number of labeled rooted trees with 3-colored leaves.

G.f.: B(x/(1-x)) where B is g.f. of A000169.

Number of labeled trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

Number of labeled planted trees with 2-colored leaves.

Number of labeled trees with 2-colored leaves.

Number of n-node rooted trees with nodes of 2 colors.

Number of trees with n 2-colored nodes.

a(n) = 2^n*n^(n-1).

Number of labeled trees with 2-colored nodes.

Number of rooted trees with 3-colored nodes.

Number of trees with 3-colored nodes.