-561

Appears in sequences

• cos(tan(arctanh(x)))=1-1/2!*x^2-15/4!*x^4-561/6!*x^6-38623/8!*x^8...at n=3A012178
• Expansion of Product_{m>=1} (1-m*q^m)^22.at n=4A022682
• a(n) = A000217(n) - A048702(n).at n=68A075113
• a(n) = -Sum_{d|n} (-n/d)^d.at n=15A076717
• Alternating sum of squares to n.at n=32A089594
• Triangular sequence of coefficients of a polynomial recursion for C_n and B_n Cartan matrices: p(x, n) = (-2 + x)*p(x, n - 1) - p(x, n - 2) p(x,n)=x2-4*x+4-m:m=5;(related sequence: A_n:m=1,G_n,m=3,B_n,C_n,m=2) This triangular sequence is an extension to the Cartan pattern of matrices.at n=57A136321
• a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3).at n=41A165192
• Triangle, read by rows, T(n, k) = p(n)/(p(k)*p(n-k)), where p(n) = Product_{j=1..n} A001607(j).at n=58A177693
• Triangle, read by rows, T(n, k) = p(n)/(p(k)*p(n-k)), where p(n) = Product_{j=1..n} A001607(j).at n=62A177693
• Numerators of coefficient array for minimal polynomials of sin(2*Pi/n). Rising powers of x.at n=92A181872
• a(n) = (-1)^(n-3)*binomial(n,3) - 1.at n=13A216414
• Values of n such that L(19) and N(19) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.at n=5A227522
• Alternating sum of heptagonal numbers.at n=21A266085
• Convolution square of A112274.at n=30A285355
• G.f. A(x) satisfies: [x^k] (1+x)^(n^2) * A(x) = 0 for k = (n-1)^2 + 1 through k = n^2 for n >= 1.at n=7A305600
• G.f.: A(x,y) = Sum_{n=-oo..+oo} (-1)^n * (x*y)^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108), as a triangle of coefficients T(n,k) of x^n*y^k in A(x,y), read by rows n >= 0.at n=37A355344
• G.f.: Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^(3*n-3), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).at n=13A355348
• G.f.: Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^(3*n-3), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).at n=31A355348