-453

Appears in sequences

• Expansion of e.g.f. log(cosh(x)-log(x+1)).at n=6A013497
• Coefficients of the '6th-order' mock theta function phi(q).at n=53A053268
• McKay-Thompson series of class 14a for Monster.at n=7A058505
• Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 5.at n=33A060024
• Expansion of g.f. (1+x^2)/(1+x-x^3).at n=45A104770
• Expansion of 1/(x^5 - 2*x^4 + x^3 - 2*x^2 + x - 1).at n=25A129704
• Triangle of coefficients of Hermite-like analog of A053120 Chebyshev's T(n, x) polynomials (powers of x in increasing order): p(x,n)=2*x*p(x,n-1)-n*p(x,n-2).at n=29A136665
• Expansion of f(x, x^7) / f(x, x^3) in powers of x where f(, ) is Ramanujan's general theta function.at n=53A259774
• Triangle of coefficients of Gaussian polynomials [2n+5,5]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,...,g with g=5n.at n=39A267485
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 414", based on the 5-celled von Neumann neighborhood.at n=34A272015
• Inverse Euler transform of the sum-of-divisors or sigma function A000203.at n=40A320780
• Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} sigma(n) * x^n, where sigma = A000203.at n=40A328776
• T(n, k) = A343277(n)*[x^k] p(n, x) where p(n, x) = (1/(n+1))*Sum_{k=0..n} (-1)^k*E1(n, k)*x^(n - k) / binomial(n, k), and E1(n, k) are the Eulerian numbers A123125. Triangle read by rows, for 0 <= k <= n.at n=24A342321
• For 1<=x<=n, 1<=y<=n, with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = sum of the values of u+v.at n=54A345425
• Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} sigma(n)*x^n, where sigma = A000203.at n=40A353924
• Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} sigma(n)*x^n, where sigma = A000203.at n=40A353947
• a(n) = n - A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse.at n=15A354207