-20160

Appears in sequences

• Expansion of e.g.f. sech(arcsinh(x)*arctan(x)) (only even powers).at n=5A012633
• Expansion of e.g.f. arctan(log(x+1) - arcsin(x)).at n=10A013225
• Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 4.at n=9A051685
• Triangle of coefficients of polynomials H(n,x) formed from the first (n+1) terms of the power series expansion of ( -x/log(1-x) )^(n+1), multiplied by n!.at n=29A075263
• Signed variant of A077012.at n=34A078921
• Real term generated from a complex product operation.at n=7A121735
• Expansion of e.g.f.: (1-2*x)*sqrt(1-4*x).at n=6A126089
• Irregular triangle of coefficients of a partition transform for direct Lagrange inversion of an o.g.f., complementary to A134685 for an e.g.f.; normalized by the factorials, these are signed, refined face polynomials of the associahedra.at n=14A133437
• Irregular triangle of coefficients of a partition transform for direct Lagrange inversion of an o.g.f., complementary to A134685 for an e.g.f.; normalized by the factorials, these are signed, refined face polynomials of the associahedra.at n=15A133437
• A triangular sequence from an expansion of coefficients of the function: p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=1/Sqrt[1 - 2*t^2 + t^4];g(t)=t. (Based on the Weierstrass functions of Jenkins-Serrin minimal surface.)at n=18A137523
• Triangular sequence from coefficients of the umbral calculus expansion of a Golden -Mean Bernoulli function(A001898): p(x,t)=t*phi^(x*t)/(phi^t - 1), where the golden ratio replaces "e".at n=23A137524
• A triangle of infinite sum coefficients with: Limit[Log[1-x],x->0]=-x: p(x,y)=1+n!*x^(n - 1)*Sum[x^k/(k*Binomial[n + k, k]), {k, 1, Infinity}]; such that Log[1-x]->-x.at n=37A157047
• A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n).at n=30A158452
• A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n).at n=31A158452
• A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n).at n=32A158452
• A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n).at n=35A158452
• A triangle related to the GF(z) formulas of the rows of the ED1 array A167546.at n=30A167556
• Triangle read by rows: T(n,k) = n!*S(n,k), where S(n,k) is the matrix inverse of the triangle zeta(k-n,1) - zeta(k-n,k+1), n>=1, k>=1.at n=34A214435
• Expansion of q * (phi(q) * psi(-q))^8 in powers of q where phi(), psi() are Ramanujan theta functions.at n=29A216711
• E.g.f.: exp(x^3/(1 + x + x^2 + x^3)).at n=8A293590