158720

Appears in sequences

• a(n) = n*(n+1)*(n+2)^2/6.at n=30A004320
• Triangle T(n,k) read by rows; related to number of preorders.at n=23A079507
• Numerator of 2*n*A000111(n-1)/A000111(n): approximations of Pi, using Euler (up/down) numbers.at n=9A132049
• Number of 1..20 integer arrays v[1..n] of length n with all autocorrelation values sum(i){v[i]*v[i-k]} distinct for k in 0..n-1.at n=3A171294
• Number of 1..n integer arrays v[1..4] of length 4 with all autocorrelation values sum(i){v[i]*v[i-k]} distinct for k in 0..3.at n=19A171341
• Numbers with 44 divisors.at n=27A175751
• Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive step pattern up, down, up, down; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-3)/2)), read by rows.at n=22A230797
• Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=up and 0=down; triangle T(n,k), n>=0, read by rows.at n=24A242783
• a(n) = 27*(n - 6)^2 + 4*(n - 6)^3 = ((n - 6)^2)*(4*n + 3).at n=38A245032
• Number of permutations of [n] with exactly three (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=up and 0=down.at n=3A246223
• Terms satisfy: a(2*n) = a(n)*b(n) and a(2*n+1) = a(n+1)*b(n) for n>=0 with a(0)=1, where A(x)^2 = Sum_{n>=0} b(n)*x^n and g.f. A(x) = Sum_{n>=0} a(n)*x^n.at n=15A265264
• a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).at n=15A329929
• a(n) = lcm(n, tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).at n=15A334985
• a(n) = lcm(tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).at n=15A336723
• a(n) = A341886(n)/2; numbers k such that A307437(k) is even.at n=27A341887