-867

Appears in sequences

• Triangle read by rows: first define the Narayana numbers: Y(n,m)=Binomial[n, m]*Binomial[n + 1, m + 1]/(n - m + 1); then t(n,m)=Sum[(-1)^j *Y(n + 1, j)*(k + 1 - j)^n, {j, 0, k + 1}].at n=17A155796
• Triangle, read by rows, T(n, k) = Sum_{j=0..k} (-1)^j*(k-j+1)^n*binomial(n+1, j) *binomial(n+2, j)/(j+1).at n=23A176124
• Discriminant of the pure cubic field Q(m^(1/3)), where m = A004709(n) is the n-th cubefree number.at n=14A242867
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 233", based on the 5-celled von Neumann neighborhood.at n=21A270979
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 358", based on the 5-celled von Neumann neighborhood.at n=43A271413
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 453", based on the 5-celled von Neumann neighborhood.at n=17A272276
• A signed variant of A309132.at n=50A326582
• Expansion of 1 / (1 + Sum_{p prime, k>=1} x^(p^k)).at n=43A329098
• Values z of primitive solutions (x, y, z) to the Diophantine equation x^3 + y^3 + 2*z^3 = 1458.at n=49A336226
• a(1) = 1, a(2) = 3; a(n) = n^2 * Sum_{d|n, d < n} (-1)^(n/d) a(d) / d^2.at n=33A361986
• G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 3*x^k)) ).at n=10A363581