-2688

Appears in sequences

• Expansion of log(1+x)/cosh(log(1+x)).at n=8A009430
• sin(arctan(x)*tan(x))=2/2!*x^2+40/6!*x^6-2688/8!*x^8-31712/10!*x^10...at n=3A012445
• arcsin(arctan(x)*tan(x))=2/2!*x^2+280/6!*x^6-2688/8!*x^8+1016608/10!*x^10...at n=3A012446
• arctan(arctan(x)*tan(x))=2/2!*x^2-80/6!*x^6-2688/8!*x^8+260608/10!*x^10...at n=4A012447
• sinh(arctan(x)*tan(x))=2/2!*x^2+280/6!*x^6-2688/8!*x^8+774688/10!*x^10...at n=3A012449
• arcsinh(arctan(x)*tan(x))=2/2!*x^2+40/6!*x^6-2688/8!*x^8+210208/10!*x^10...at n=3A012450
• tanh(arctan(x)*tan(x))=2/2!*x^2-80/6!*x^6-2688/8!*x^8+18688/10!*x^10...at n=3A012451
• arctanh(arctan(x)*tan(x))=2/2!*x^2+400/6!*x^6-2688/8!*x^8...at n=4A012452
• Ooguri-Vafa invariants of disk degeneracies for brane III in the O(K) -> P^1 x P^1 geometry.at n=3A092706
• G.f. A(x) satisfies: 3^n - 1 = Sum_{k=0..n} [x^k]A(x)^n and also satisfies: (3+z)^n - (1+z)^n + z^n = Sum_{k=0..n} [x^k](A(x)+z*x)^n for all z, where [x^k]A(x)^n denotes the coefficient of x^k in A(x)^n.at n=12A100225
• Riordan array ((3-sqrt(1+8x))/2, (sqrt(1+8x)-1)/4).at n=22A122440
• Triangle a(n,k) of the expansion coefficients of the Hermite polynomial 2*H(n/2,x) if n even, of H((n-1)/2,x)+H((n+1)/2,x) if n odd.at n=68A139158
• A triangle of coefficients from Hermite polynomials A060821 as {x,y},{y,z},{z,x} binomials reduced to x: f(x,y,n)=Sum[Coefficients(H(x,n))(i)*x^i*y^(n-1),{i,0,n}]; p(x,y,z)=f(x,y,n)+f(y,z,n)+f(z,x,n).at n=33A139583
• Triangle T(n, k) = coefficients of p(n, x), where p(n, x) = (-1)^n*(x+2-n)*(x+2)^(n-1), p(0, x) = 1, and p(1, x) = -1-x, read by rows.at n=39A158285
• Coefficients of minimal polynomials with roots a(n)=(1 + Prime[n]^(1/n))/2: p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]].at n=51A174543
• Coefficients of minimal polynomials with roots a(n)=(1 + Prime[n+1]^(1/n))/2: p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n+1]^(1/n))/2, x]].at n=51A174547
• A symmetrical triangle sequence:t(n,m)=(-1)^m*(n - m)!*Binomial[n - 1, m] + (-1)^(n - m + 1)*(n - (n - m + 1))!*Binomial[n - 1, n - m + 1].at n=24A176862
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of {|i-j}, (A049581).at n=40A203993
• Triangle read by rows: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min(2i-1,2j-1) (A157454).at n=41A204021
• Triangle read by rows, T(n,k) = (-1)^(n-k)*C(n,k)*k^n, for n >= 0 and 0 <= k <= n.at n=30A258773