155584

Appears in sequences

• Number of partitions of n into parts of 16 kinds.at n=6A023014
• Distinct even numbers in the numerators of the 1/3-Pascal triangle (by row).at n=45A046559
• Distinct even numbers in writing first numerator and then denominator of each element to the right of the central elements of the 1/3-Pascal triangle (by row).at n=31A046562
• Number of sequences {s(i): i=0..n} such that |s(i)-s(i-1)|=1, i=1..n and s(i)=0 at four values of i, one of which is i=0.at n=19A052207
• 3-apexes of Omega: numbers k such that Omega(k-3) < Omega(k-2)< Omega(k-1) < Omega(k) > Omega(k+1) > Omega(k+2) > Omega(k+3), where Omega(m) = the number of prime factors of m, counting multiplicity.at n=36A076760
• Binomial transform of A004524 starting at 1.at n=15A132402
• a(n) = x(n) * 2^((n mod 2 - 1)/2), with x(n)=Sum(x(k)*x(n-k-1):0<=k<n), x(0)=SQRT(2).at n=9A137697
• a(n) = (n-1)^2*binomial(2n,n)/(2*(n+1)).at n=8A145885
• Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>3z.at n=34A212514
• E.g.f.: exp( Sum_{n>=1} A000108(n-1)*x^n/n ), where A000108(n) = binomial(2*n,n)/(n+1) forms the Catalan numbers.at n=7A243953
• Table of coefficients in functions R(n,x) defined by R(n,x) = exp( n*x*G(n,x)^(n-1) ) / G(n,x)^(n-1) where G(n,x) = 1 + x*G(n,x)^n, for rows n>=1.at n=43A251660
• Triangle T read by rows: T(n,k) = binomial(2*n+1,k)*binomial(n,k), n>=0, 0<=k<=n.at n=43A252501
• Starting a random walk on Z at 0 triangle T(j,k) gives the number of paths of length 2*j returning to 0 exactly k times.at n=58A276418
• Number of subsets of {1..n} such that every pair of distinct elements has a different quotient.at n=20A325860