353792

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=11A000111
• Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).at n=5A000182
• Triangle of coefficients in expansion of D^n (tan x) in powers of tan x.at n=35A008293
• 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=29A008303
• 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=35A008303
• Triangle of tangent numbers.at n=30A008308
• Triangle T(n,k) = P(n,k)/2, n >= 2, 1 <= k < n, of one-half of number of permutations of 1..n such that the differences have k runs with the same signs.at n=54A008970
• Expansion of e.g.f.: 1 + tan(x).at n=11A009006
• Expansion of log(1+tanh(tan(x))).at n=11A009386
• Expansion of e.g.f.: tan(x)*(1+x).at n=11A009725
• Expansion of e.g.f. tan(x)^2 (even powers only).at n=5A009764
• Triangle of Euler-Bernoulli or Entringer numbers.at n=55A010094
• Expansion of cos x + tan x + sec x.at n=11A029584
• Triangle T(n,k) (1 <= k <= n) of tangent numbers, read by rows: T(n,k) = coefficient of x^n/n! in expansion of (tan x)^k/k!.at n=55A059419
• Triangle T(n,k) generalizing the tangent numbers.at n=15A064190
• Triangle read by rows, T(n,k) = 2^(n-k)*[x^k] Euler_polynomial(n, x), for n >= 0, k >= 0.at n=66A081733
• 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=15A085734
• T(n, k) = [x^k] (2*n)! [z^(2*n)] 1/cos(z)^x, triangle read by rows, for 0 <= k <= n.at n=22A088874
• Triangle read by rows: T(n,k) is the number of down-up permutations on [n] with k left-to-right maxima.at n=36A098906
• Triangle T(n,k) (n >= 1, 0 <= k <= floor((n-1)/2)) read by rows, where T(n,k) = (k+1)T(n-1,k) + (2n-4k)T(n-1,k-1).at n=35A101280