-1088

Appears in sequences

• Low temperature series associated with square lattice.at n=8A047710
• Expansion of 1/(1-2x+2x^4).at n=18A090399
• Triangle read by rows of coefficients of Chebyshev-like polynomials P_{n,5}(x) with 0 omitted (exponents in increasing order).at n=39A136397
• A triangular sequence based on second integer differential using columns n and rows m, in the ChebyshevT T(n,m): d20(n,m)=T(n+2,m)-2*T(n+1,m)+T(n,m); d02(n,m)=T(n,m+2)-2*T(n,m+1)+T(n,m); D2(n,m)=d20(n,m)+d02(n,m).at n=27A140877
• Irregular triangle, T(n, k) = coefficients of p(x, n), where p(x, n) = (1-2*x)^(n+1) * Sum_{j>=0} j^n*(x/(1-x))^j, read by rows.at n=31A142073
• Irregular triangle, T(n, k) = [x^k] p(n, x), where p(n, x) = 4*Sum_{j=0..n} A008292(n+1, j) * (x/2)^j * (1-x/2)^(n-j), read by rows.at n=28A147563
• The n-th term of the n-th Dirichlet self-convolution equals n^2.at n=33A163591
• A triangle of coefficients based on the squares of the Chebyshev T and U polynomials: p(x,n)=If[Mod[n, 2] == 0, (ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2), (-1 + ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2)].at n=29A173335
• Expansion of (k(q) / 4)^4 in powers of q where k() is a Jacobi elliptic function.at n=3A225915
• a(n) = 1 - n^2.at n=33A258837
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 179", based on the 5-celled von Neumann neighborhood.at n=19A270625
• Triangle read by rows, T(n, k) = Sum_{j=0..n} (-1)^(k-j)*Eulerian1(n, j)* binomial(n-j, n-k) for 0 <= k <= n.at n=34A291977
• Irregular array related to the Euler numbers, read by rows, T_row(n) = A326722_row(2*n) + A326722_row(2*n+1) for n >= 0, T_row(-1) = [1].at n=18A326721
• Irregular array related to the Euler numbers, read by rows, T_row(n) = A326722_row(2*n) + A326722_row(2*n+1) for n >= 0, T_row(-1) = [1].at n=22A326721
• T(n, k) = n! * [x^k] [y^n] sec(z)(x + z*sin(z)/y) where z = y*sqrt(x^2 - 1) for 0 <= k <= n+1 and T(-1, 0) = 1, triangle read by rows.at n=38A326722
• T(n, k) = n! * [x^k] [y^n] sec(z)(x + z*sin(z)/y) where z = y*sqrt(x^2 - 1) for 0 <= k <= n+1 and T(-1, 0) = 1, triangle read by rows.at n=42A326722
• Triangle read by rows: T(n, k) = (-1)^(n - k) * binomial(n, k) * A000182(n).at n=11A326723
• Triangle read by rows: T(n, k) = (-1)^(n - k) * binomial(n, k) * A000182(n).at n=13A326723
• a(n) = Sum_{d|n} mu(d) * binomial(d+n/d-1, d).at n=50A338657
• a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).at n=64A368922