-1584

Appears in sequences

• E.g.f.: sin(arctanh(x)*log(x+1)) = 2/2!*x^2 - 3/3!*x^3 + 16/4!*x^4 - 50/5!*x^5 + ...at n=8A012698
• arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...at n=8A012704
• Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^3.at n=31A029840
• Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 6.at n=40A060025
• Sum_{k=1..2n-1} J(4*n,k)*k^2, where J(i,j) is the Jacobi symbol.at n=32A097544
• E.g.f.: 3x/(-1+1/(-1+1/(-1+log(1+3x)))) = -3x[2-log(1+3x)]/[3-2log(1+x)].at n=6A109590
• Coefficient table for polynomials related to the eigenfunctions of a certain Schroedinger problem (Poeschl-Teller I).at n=38A130415
• Triangle of coefficients of the Pascal sum of A053120 Chebyshev's T(n, x) polynomials :p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}].at n=49A136663
• Triangle of coefficients of the Pascal sum of A053120 Chebyshev's T(n, x) polynomials :p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}].at n=50A136663
• A triangle of coefficients of A053122 type binomials {x,y},{y,z} and {z,x}, made using A_n Cartan type matrix characteristic polynomials: an(x,n) = CharacteristicPolynomial(M(A_n,n)); f(x,y,n) = Sum[Coefficients(an[x,n)*x^i*y^(n-i),{i,0,n}]; p(x,y,z,n) = f(x,y,n) + f(y,z,n) + f(z,x,n).at n=39A139584
• Composition of Catalan and Fibonacci numbers.at n=76A189675
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min{i-j+1,j-i+1} (A203994).at n=29A203995
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 43", based on the 5-celled von Neumann neighborhood.at n=23A269879
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled von Neumann neighborhood.at n=27A271015
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 427", based on the 5-celled von Neumann neighborhood.at n=31A272110
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 597", based on the 5-celled von Neumann neighborhood.at n=43A273147
• E.g.f. A(x) satisfies: A( x*exp(x)*cosh(x) ) = x*exp(2*x).at n=5A276359
• Expansion of phi(x)^6 * phi(-x)^2 in powers of x where phi() is a Ramanujan theta function.at n=41A291124
• Expansion of phi(-x^9) * f(-x^3)^2 / f(-x^2)^3 in powers of x where f(), phi() are Ramanujan theta functions.at n=19A298733
• G.f.: Sum_{n>=1} (-1)^(n-1) * x^(n^2)/(1 - x^n)^n.at n=91A303506