-628

Appears in sequences

• G.f.: 1/(1 - x^3 - 2 x^4 + x^5).at n=33A122517
• Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial h(n,x) with h(0,x)=1, h(1,x)=1-x and recursively h(n,x) = 1 + n -(1-x)*(1-h(n-1,x)) - n*h(n-2,x).at n=48A136247
• Characteristic polynomials of a binomial modulo two Hadamard transpose general matrix: t(n,m,d) = If[ m <= n, binomial(n, m) mod 2], 0]; M(d)=t(n,m,d).Transpose[t(n,m,d)].at n=48A158188
• Express the Sum_{n>=0} p(n)*x^n, where p(n) is the partition function, as a product Product_{k>=1} (1 + a(k)*x^k).at n=25A220420
• 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=36A220861
• a(n) = Sum_{k=0..n} (-1)^k*k*Fibonacci(k), where Fibonacci(k) = A000045(k).at n=11A263878
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 286", based on the 5-celled von Neumann neighborhood.at n=44A271124
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 419", based on the 5-celled von Neumann neighborhood.at n=19A272048
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 598", based on the 5-celled von Neumann neighborhood.at n=23A273152
• Expansion of Product_{k>=1} ((1 - x^(2*k))/(1 - x^(2*k-1)))^k.at n=53A296046
• a(n) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 + ... - (up to the n-th term).at n=36A319885
• Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x + 2*x^2)^2).at n=15A322040
• G.f.: Sum_{n>=0} x^n * (x^(n+1) + i)^n / (1 + i*x^(n+1))^(n+1).at n=38A324300
• a(1) = 1; a(n+1) = a(n) +- (sum of digits of a(1) up to a(n)), with "+" when a(n) is odd, or "-" if even.at n=24A332058
• Product_{n>=1} 1 + a(n)*x^n = Sum_{n=-oo..oo} x^(n^2) = theta_3(x).at n=12A342223