-692

Appears in sequences

• Expansion of (1-x)/(1-x+x^2+x^3).at n=23A078016
• Expansion of (1-x)/(1 + x + x^2 - x^3).at n=21A078046
• Expansion of q^(-1) * f(-q^2, -q^5)^2 * f(-q^3, -q^4) / f(-q^1, -q^6)^3 in powers of q where f() is Ramanujan's two-variable theta function.at n=42A108481
• Expansion of phi(-q) / phi(q^4) in powers of q where phi() is a Ramanujan theta function.at n=41A208604
• Choose smallest m>0 such that the n-th rational prime p ramifies in the imaginary quadratic extension field K = Q(sqrt(-m)); a(n) = discriminant(K).at n=39A220861
• Expansion of q^(-1) * f(-q^3, -q^4)^3 / (f(-q^1, -q^6)^2 * f(-q^2, -q^5)) in powers of q where f() is Ramanujan's two-variable theta function.at n=42A246713
• Expansion of Product_{k>=1} ((1 - k*x^k) / (1 - x^k)).at n=21A267005
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 150", based on the 5-celled von Neumann neighborhood.at n=37A270324
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 294", based on the 5-celled von Neumann neighborhood.at n=43A271135
• a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).at n=3A307318
• A(n,k) = Sum_{i_1=0..n} Sum_{i_2=0..n} ... Sum_{i_k=0..n} (-1)^(i_1 + i_2 + ... + i_k) * multinomial(i_1 + i_2 + ... + i_k; i_1, i_2, ..., i_k), square array A(n,k) read by antidiagonals, for n >= 0, k >= 0.at n=24A308322
• a(n) = Sum_{i_1=0..n} Sum_{i_2=0..n} ... Sum_{i_n=0..n} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).at n=3A308323
• G.f. satisfies A(x) = 1 + x * A(x * (1 - x^3)).at n=18A360897