-3456

Appears in sequences

• sin(arctan(x)^2)=2/2!*x^2-16/4!*x^4+248/6!*x^6-3456/8!*x^8...at n=3A012457
• Arcsinh(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 248/6!*x^6 - 3456/8!*x^8 + ...at n=4A012462
• a(n) = n!*Sum_{k=1..n} mu(k)/k, where mu(k) is the Möbius function.at n=8A068337
• Expansion of (1-x)/(1-2*x^2+2*x^3).at n=15A078025
• Expansion of (1-x)/(1+2*x^2+x^3).at n=23A078036
• Coefficients for obtaining A120057 from Bell numbers.at n=52A120058
• Triangle read by rows: T(n, k) is the coefficient of x^k in the polynomial 1 - T_n(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.at n=44A123583
• Triangle read by rows: T(n, k) is the coefficient of x^k in the polynomial 1 - ChT(n, x^(1/2))^2, where ChT(n, x) is the n-th Chebyshev polynomial of the first kind, evaluated at x (0 <= k <= n).at n=25A123588
• Triangle of coefficients of even modified recursive orthogonal Hermite polynomials given in Hochstadt's book:P(x, n) = x*P(x, n - 1) - n*P(x, n - 2) ;A137286; P2(x,n)=P(x,n)+P(x,n-2).at n=55A136586
• C(n+7, 7)*(n+4)*(-1)^(n+1)*16.at n=2A138332
• A triangle of coefficients of a Moebius-transformed Pascal triangle as a sum: b(x,y,n)=Sum[Binomial[n,i]*x^i*y^(n-i),{i,0,n}]; transforms: x'->(a1*x + b1)/(c1*x + d1); y'->(a2*y + b2)/(c2*y + d2); b1(x,y,n)=(c1*x + b1)^(k)*(c2*y + d2)^(k)*b(x',y',n); f(x,y,z,n)=b1(x,y,n)+b1(y,z,n)+b1(z,x,n).at n=11A139815
• Antidiagonal expansion of rational polynomial with factors: p(x,n) = If[n == 0, 1/(1 - x), x*ChebyshevU[n, x]/ChebyshevT[n + 1, x]].at n=38A173293
• a(n) = p(n) - p(n-1) - p(n-2) + p(n-5), where p(n) = A000041(n).at n=38A195054
• Coefficients of recurrence for rows and columns of A250544 and rows of A250691.at n=16A255002
• (Sum_{t=0..oo} ((-1)^t*(2*t+1)*q^((2*t+1)^2)))^3 * (Sum_{t=0..oo} q^((2*t+1)^2)) = Sum_{k=0..oo} a(k)*q^(8*k+4).at n=38A322031
• G.f.: Sum_{n>=0} (n+1) * x^n * (1 + x^n)^n / (1 + x^(n+1))^(n+2).at n=35A326285
• El Gradechi's hybrid coefficients alpha^{4,6}_n.at n=1A331769
• Triangle read by rows. T(n, k) are the coefficients of polynomials p_n(x) based on the Eulerian numbers of second order representing the Bernoulli numbers as B_n = p_n(1) / (2*(2*n - 1)!).at n=13A356547
• Expansion of g.f. A(x) satisfying Sum_{n>=0} Product_{k=1..n} (x^(2*k-1) + A(x)) = Product_{k>=1} (1 - x^(2*k)) * (1 + x^k + A(x))^2 / (1 + x^(2*k) + A(x))^2.at n=5A370344
• a(n) = Sum_{i=1..n} (Product_{j=1..n} M(j, ((i+j-2) mod n)+1) - Product_{j=1..n} M(j, ((i-j-1) mod n)+1)) where M is the n X n matrix with numbers 1, 2, ..., n^2 in order across rows.at n=6A389261