-394

Appears in sequences

• Inverse of coordination sequence array A113413.at n=15A080245
• Difference of the first two Stirling numbers of the first kind.at n=5A081046
• Expansion of (1-x+sqrt(1-6x+x^2))/2 in powers of x.at n=6A085403
• Expansion of (1 + x + sqrt(1 - 6*x + x^2))/2 in powers of x.at n=6A086456
• Triangle, read by rows, where T(n,k) = (k/n)*Sum_{d|n} A096797(d,k).at n=56A096798
• Riordan array ((1-x+sqrt(1+6*x+x^2))/2, (sqrt(1+6*x+x^2)-x-1)/2).at n=21A112477
• Expansion of (1 + x + sqrt(1 + 6*x + x^2))/2.at n=6A112478
• Riordan array ((1-x+sqrt(1-6x+x^2))/2, (1+x-sqrt(1-6x+x^2))/4).at n=21A117354
• Triangle T(n,k), read by rows, defined by T(n,k)=3*T(n-1,k)-T(n-1,k-1)-T(n-2,k), T(0,0)=1, T(1,0)=2, T(1,1)=-1, T(n,k)=0 if k<0 or if k>n.at n=24A123971
• Triangle, matrix inverse of A124733, companion to A123965.at n=24A126124
• G.f. A(x) satisfies: [x^n] A(x)^(2^n) = 4^n for n>=0.at n=4A134046
• Stirling-like triangle by rows generated from (x-1)*(x-1)*(x-2)*(x-3)*(x-4)*...at n=26A158471
• The n-th term of the n-th Dirichlet self-convolution equals n^2.at n=15A163591
• Expansion of phi(q^2)^2 / (phi(q) * phi(q^4)) in powers of q where phi() is a Ramanujan theta function.at n=9A232358
• 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=25A285635
• Expansion of Sum_{k>=1} mu(k)*log((theta_3(x^k) + 1)/2)/k, where theta_3() is the Jacobi theta function.at n=38A308297
• G.f.: Sum_{n>=0} (x^(2*n-1) + 1)^n * x^n / (1 + x^(2*n+1))^(n+1), an even function.at n=30A326602
• Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.at n=19A353925
• Martingale win/loss triangle, read by rows: T(n,k) = total number of dollars won (or lost) using the martingale method on all possible n trials that have exactly k losses and n-k wins, for 0 <= k <= n.at n=52A355659
• Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).at n=15A356907