-1360

Appears in sequences

• a(n) = Sum_{d|n, d == 1 mod 4} d^2 - Sum_{d|n, d == 3 mod 4} d^2.at n=38A002173
• Expansion of e.g.f.: cosh(sin(x))/exp(x).at n=9A009145
• Expansion of log(1+sinh(tanh(x))).at n=8A009349
• a(n) = determinant of n X n circulant matrix whose first row is the first n triangular numbers A000217(0), A000217(1), ... A000217(n-1).at n=3A118705
• Irregular triangle, read by rows: T(n, k) = [x^k]( y(n, x) ), where y(n, x) = - 2*y(3, x) - x*y(n-1, x) + 2*x^2*y(n-1, x) + x^2*y(n-2, x), and y(1, x) = -8 - 3*x + 8*x^2, y(2, x) = 4 - 4*x - 10*x^2 + 4*x^3 + 4*x^4, y(3, x) = -8 + 4*x + 24*x^2 - 9*x^3 - 24*x^4 + 4*x^5 + 8*x^6.at n=74A131641
• A triangular sequence from 2^n times the coefficients of characteristic polynomials of a rational tridiagonal matrix type: M(3)= {{1/2,-1,0} {-1,1/2,-m}, {0,-1,1/2}}};m=-1; polynomial recursion associated is: p(x, n) = (1 - 2*x)*p(x, n - 1)/2 - p(x, n - 2);.at n=32A136330
• Expansion of q^(-1/2) * (eta(q)^4 * eta(q^4)^2 / eta(q^2)^3)^2 in powers of q.at n=19A138502
• Expansion of ((phi(q) * phi(-q^2)^2)^2 - 1) / 4 in powers of q where phi() is a Ramanujan theta function.at n=38A138505
• Triangle formed by coefficients of the expansion of p(x, n), where p(x,n) = (1 + 2*x - x^2)^(n + 1)*Sum_{j >= 0} (j+1)^n*(-2*x + x^2)^j.at n=46A156901
• A triangle related to the a(n) formulas of the rows of the ED1 array A167546.at n=39A167552
• The fourth left hand column of triangle A167552.at n=5A168302
• Inverse binomial transform of -2 followed by A000032(n+1).at n=15A244213
• Expansion of q^(-1/4) * eta(q)^8 * eta(q^4)^2 / eta(q^2)^5 in powers of q.at n=33A244276
• Difference between sums of quadratic residues and non-residues modulo n that are coprime to n.at n=84A255643
• Difference between sums of quadratic residues and non-residues modulo n (residues are not necessarily coprime to n).at n=84A255644
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 267", based on the 5-celled von Neumann neighborhood.at n=19A271086
• a(n) = n^4 * Sum_{d|n} (-1)^(n/d + 1) * mu(d) / d^4.at n=5A338549
• G.f. A(x) satisfies: A(x) = A(x^3 - x^6)/x^2.at n=15A350481
• a(n) = A353750(n) - A353749(n).at n=40A353757
• Expansion of g.f. A(x) satisfying A(x) = A(x^2) - x*A(x^2)^2.at n=61A374571