-6561

Appears in sequences

• Expansion of bracket function.at n=15A000748
• a(n) = Sum_{j=0..floor(n/3)} (-1)^j*binomial(n,3*j).at n=17A057681
• a(n) = Sum_{j=0..floor(n/3)} (-1)^j*binomial(n,3*j+1).at n=18A057682
• A transform of the Jacobsthal numbers.at n=18A103312
• Triangle read by rows: T(n,k) = (-1)^k*3^(n-1-2k)*binomial(n-k,k)*(4n-5k)/(n-k) (0 <= k <= floor(n/2), n >= 1).at n=21A104063
• Expansion of (1+2*x)/(1+3*x+3*x^2).at n=16A123877
• a(n) = the numerator of b(n): {b(n)} is such that the continued fraction (of rational terms) [b(1);b(2),...,b(n)] equals the n-th prime, for every positive integer n.at n=30A128270
• a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), a(0)=a(1)=a(2)=1.at n=37A131292
• Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 3^(n - 1), T(n,k) = -3^(n - k - 1), 1 <= k <= n - 1.at n=56A152570
• Triangle, T(n, k, q) = e(n, k, q), where e(n, k, q) = ((1 - (-q)^k)/(1+q))*e(n-1, k, q) + (-q)^(k-1)*e(n-1, k-1, q), e(n, 0, q) = e(n, n, q) = 1, and q = 2, read by rows.at n=47A156535
• a(n) = 3*a(n-2) for n > 2; a(1) = 3, a(2) = -1.at n=17A162852
• Numerators to Dirichlet inverse of Euler totient based version of series expansion for x/LambertW(x).at n=10A230283
• Expansion of (4+3*x)/(1+3*x).at n=7A256096
• Expansion of Product_{k>=1} (1 - 3^(k-1)*x^k).at n=12A352786
• Irregular triangle T(n,k), n >= 0, 0 <= k <= 2*n+1, read by rows, where T(n,k) = [x^k] (1-x)^(n+1) * Sum_{k=0..n} (2*k+1)^n * x^k.at n=29A382289