22368256

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=13A000111
• Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).at n=6A000182
• Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.at n=41A008303
• Triangle of tangent numbers.at n=42A008308
• Expansion of e.g.f.: 1 + tan(x).at n=13A009006
• Expansion of log(1+tanh(tan(x))).at n=13A009386
• Expansion of log(1+tanh(tanh(x))).at n=13A009387
• Expansion of e.g.f.: tan(x)*(1+x).at n=13A009725
• Expansion of e.g.f. tan(x)^2 (even powers only).at n=6A009764
• exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...at n=13A012253
• Expansion of cos x + tan x + sec x.at n=13A029584
• Triangle T(n,k) generalizing the tangent numbers.at n=21A064190
• 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=21A085734
• T(n, k) = [x^k] (2*n)! [z^(2*n)] 1/cos(z)^x, triangle read by rows, for 0 <= k <= n.at n=29A088874
• a(n) = 2^n*E(n, 1) where E(n, x) are the Euler polynomials.at n=13A155585
• The EG1 triangle.at n=21A162005
• Number of 6-elements orbits of S3 action on irreducible polynomials of degree n > 1 over GF(2).at n=30A165921
• a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 20.at n=6A166984
• Number of permutations of 1..n having exactly 6 maxima.at n=2A179709
• Number of permutations of 1..n having exactly 7 maxima.at n=1A179710