-1640

Appears in sequences

• sin(arcsinh(x)+arcsin(x))=2*x-8/3!*x^3+50/5!*x^5-1640/7!*x^7...at n=3A013085
• a(n) = (1 - (-3)^n)/4.at n=8A014983
• Triangle of q-binomial coefficients for q=-3.at n=37A015110
• Triangle of q-binomial coefficients for q=-3.at n=43A015110
• Gaussian binomial coefficient [ n,7 ] for q = -3.at n=1A015340
• Low temperature series for spin-1/2 Ising partition function on 5D simple cubic lattice.at n=18A030047
• "Real rabbits": a(n) = Re(c(n)) where complex c(n) = a(n) + i*b(n) and c(0) = i, c(1) = -i, c(n) = c(n-1) + i*c(n-2).at n=25A058184
• Sum_{d divides n} d^2*(-1)^bigomega(d), where bigomega(n) = A001222(n).at n=47A076792
• Matrix inverse of triangle A104559, read by rows.at n=41A104560
• Triangle of coefficients of p(x,n) = (1/4)*(1-x)^(n+1)*Sum_{m >= 0} ((2*m- 1)^n - (2*m+3)^n)*x^m, read by rows.at n=36A154852
• Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + ... + x^n to the polynomial A_k*(x+3)^k for 0 <= k <= n.at n=28A248811
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 513", based on the 5-celled von Neumann neighborhood.at n=46A272704
• E.g.f. B = B(x,y) satisfies: A^2 + B^2 + C^2 = 1 + y^2 and A^3 + B^3 + C^3 = 1 + y^3, where functions A = A(x,y) and C = C(x,y) are described by A278885 and A278887, respectively.at n=84A278886
• Triangle, read by rows, defined by recurrence: T(n,k) = T(n-1,k-1) + (-1)^k * (2 * k + 1) * T(n-1,k) for 0 < k < n with initial values T(n,0) = T(n,n) = 1 for n >= 0 and T(i,j) = 0 if j < 0 or j > i.at n=37A346083
• Expansion of Sum_{k>0} k * x^k/(1 + x^k)^3.at n=39A364343
• a(n) = Sum_{i=1..n} i^2*(-1)^ceiling(sqrt(i)).at n=26A392677