-637

Appears in sequences

• Expansion of Product_{n>=1} (1 - x^n)^7.at n=32A000730
• Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 5.at n=36A060024
• Seventh convolution of A115140.at n=11A115146
• Inverse of number triangle binomial(3n-k,n-k).at n=62A119302
• Expansion of g.f.: -x*(1 - 2*x + 6*x^2 - 2*x^3 + x^4)/((1-x)^3*(1+x)^4).at n=12A122576
• Expansion of -x*(2*x - 1)*(2*x^2 - 1)*(x^3 + 2*x^2 - x - 1)/((x - 1)*(x^2 + x - 1)*(x^4 - 4*x^3 - 4*x^2 + x + 1)).at n=15A122605
• For all n >= 2, Sum_{2<=k<=n, gcd(k,n)>1} a(k) = n. a(1)=1.at n=69A124386
• Numerator of Bernoulli(n, -1/10).at n=4A158995
• a(n) = (-1)^n*n*(n+1)*(2*n-5)/6.at n=12A167386
• Expansion of (1+4*x+x^2) / ((1-x)^3*(1+x)^4).at n=24A229834
• Signed version of A094953.at n=51A248345
• Difference between sums of quadratic residues and non-residues modulo n (residues are not necessarily coprime to n).at n=97A255644
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 115", based on the 5-celled von Neumann neighborhood.at n=13A270184
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 123", based on the 5-celled von Neumann neighborhood.at n=13A270213
• Expansion of 1/(1 + x/(1 + x^4/(1 + x^9/(1 + x^16/(1 + x^25/(1 + ... + x^(k^2)/(1 + ...))))))), a continued fraction.at n=40A285408
• G.f.: (1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - ...))))) * (1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + ...))))), a continued fraction.at n=24A285638
• Expansion of e.g.f. exp(x * (1 - exp(x))).at n=7A292893
• Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x^k * (1 - exp(x))).at n=43A292894
• Triangle read by rows, defined by Riordan's general Eulerian recursion: T(n, k) = (k+3)*T(n-1, k) + (n-k-2) * T(n-1, k-1) with T(n,1) = 1, T(n,n) = (-2)^(n-1).at n=18A306547
• Expansion of e.g.f. Product_{k>=1} exp(1 - exp(x^k/k)).at n=8A346057