Sequences

Number of permutations of length n with 4 consecutive ascending pairs.

Number of permutations of length n with 5 consecutive ascending pairs.

Strong pseudoprimes to base 2.

Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.

Final 2 digits of 4^n.

Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.

One-half the number of permutations of length n without rising or falling successions.

One-half the number of permutations of length n with exactly 3 rising or falling successions.

One-half the number of permutations of length n with exactly 4 rising or falling successions.

Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition.

Table of prime factors of 10^n - 1 (with multiplicity).

Irregular table read by rows: row n lists prime factors of 10^n + 1, with multiplicity.

Numbers k such that k! - (k-1)! + (k-2)! - (k-3)! + ... - (-1)^k*1! is prime.

Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n).

Numbers k such that phi(k) = phi(k+1).

Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.

Smallest k such that the product of q/(q-1) over the primes from prime(n) to prime(n+k-1) is greater than 2.

Number of permutations of length n by rises.

Number of permutations of length n by rises.

Number of permutations of length n by rises.

Number of permutations of length n by rises.

Image of n under the map n->n/2 if n even, n->3n-1 if n odd.

Number of permutations of length n by rises.

Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.

Numbers of form m*k with m+1 <= k <= 2m-1.

Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 1's and 2's.

Lah numbers: a(n) = (n-1)*n!/2.

a(n) = binomial coefficient C(n,10).

a(n) = binomial(n,11).

Number of equivalence classes of Boolean functions modulo linear functions.

Erroneous version of A028368.

Number of conjugacy classes in Restricted Affine Group on n variables.

Concatenations of cyclic permutations of initial positive integers.

Leech triangle: k-th number (0 <= k <= n) in n-th row (0 <= n) is number of octads in S(5,8,24) containing k given points and missing n-k given points.

Triangle in which k-th number (0<=k<=n) in n-th row (0<=n) is number of dodecads in Golay code G_24 containing k given points and missing n-k given points.

Triangle in which k-th number (0<=k<=n) in n-th row (0<=n) is number of hexads in S(5,6,12) containing k given points and missing n-k given points.

4-dimensional pyramidal numbers: a(n) = (3*n+1)*binomial(n+2, 3)/4. Also Stirling2(n+2, n).

Stirling numbers of the second kind S(n+3, n).

Stirling numbers of the second kind S(n+4, n).

Number of ways of making change for n cents using coins of 1, 5, 10, 25 cents.

Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents.

Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25 cents.

Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25, 50 cents.

Stirling numbers of first kind, s(n+3, n), negated.

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

Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)).

Number of ways of making change for n cents using coins of 1, 5, 10, 20, 50, 100 cents.

Expansion of 1/(1-x)^2/(1-x^2)/(1-x^4)/(1-x^10)/(1-x^20).

Order of Chevalley group D_n (2).

Order of real Clifford group L_n connected with Barnes-Wall lattices in dimension 2^n.