1903757312

Appears in sequences

• Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250).at n=15A000111
• Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).at n=7A000182
• Expansion of e.g.f.: 1 + tan(x).at n=15A009006
• Expansion of log(1+tanh(tan(x))).at n=15A009386
• Expansion of e.g.f.: tan(x)*(1+x).at n=15A009725
• Expansion of e.g.f. tan(x)^2 (even powers only).at n=7A009764
• Expansion of cos x + tan x + sec x.at n=15A029584
• Triangle T(n,k) generalizing the tangent numbers.at n=28A064190
• Triangle read by rows: T(0,0) = 1, T(n,k) = Sum_{j=max(0,1-k)..n-k} (2^j)*(binomial(k+j,1+j) + binomial(k+j+1,1+j))*T(n-1,k-1+j).at n=28A085734
• T(n, k) = [x^k] (2*n)! [z^(2*n)] 1/cos(z)^x, triangle read by rows, for 0 <= k <= n.at n=37A088874
• The EG1 triangle.at n=28A162005
• Expansion of e.g.f. 2*exp(x)*(1-exp(x))/(1+exp(2*x)).at n=15A163747
• Real part of the coefficient [x^n] of the expansion of (1+i)/(1-i*exp(x)) - 1 multiplied by 2*n!, where i is the imaginary unit.at n=15A163982
• Number of permutations of 1..n having exactly 7 maxima.at n=2A179710
• Array A(i,j) read by antidiagonals: A(i,j) is the (2*i-1)-th derivative of tan(tan(tan(...tan(x)))) nested j times evaluated at 0.at n=35A212267
• Shanks's array d_{a,n} (a >= 1, n >= 1) that generalizes the tangent numbers, read by antidiagonals upwards.at n=35A235606
• Array t(n,k) = k^(2n)*(k^(2n)-1)*BernoulliB(2n)/(2n), n>=1, k>=2, absolute values read by ascending antidiagonals.at n=28A241066
• Related to Euler numbers, expansion of e.g.f. tan(x)^2.at n=13A259688
• E.g.f.: S(x,k) = Integral C(x,k)*D(x,k)^2 dx, such that C(x,k)^2 - S(x,k)^2 = 1, and D(x,k)^2 - k^2*S(x,k)^2 = 1, as a triangle of coefficients read by rows.at n=35A322230
• E.g.f. C(x,y) = cos(y) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=43A324609