209865342976
domain: N
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=17A000111
- Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).at n=8A000182
- Expansion of e.g.f.: 1 + tan(x).at n=17A009006
- Expansion of log(1+tanh(tan(x))).at n=17A009386
- Expansion of log(1+tanh(tanh(x))).at n=17A009387
- Expansion of e.g.f.: tan(x)*(1+x).at n=17A009725
- Expansion of e.g.f. tan(x)^2 (even powers only).at n=8A009764
- exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...at n=17A012253
- Expansion of cos x + tan x + sec x.at n=17A029584
- a(n) = 2^n*E(n, 1) where E(n, x) are the Euler polynomials.at n=17A155585
- 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=44A212267
- Related to Euler numbers, expansion of e.g.f. tan(x)^2.at n=15A259688
- 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=44A322230
- E.g.f. C(x,y) = cos(y) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=53A324609
- E.g.f. S(x,y) = sin(x) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=36A324610
- E.g.f. C(y,x) = cos(x) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=46A324611
- E.g.f. S(y,x) = sin(y) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=44A324612
- E.g.f.: S(x,k) = -i * sn( i * Integral C(x,k) dx, k) such that C(x,k) = cn( i * Integral C(x,k) dx, k), where S(x,k) = Sum_{n>=0} Sum_{j=0..n} T(n,j) * x^(2*n+1)*k^(2*j)/(2*n+1)!, as a triangle of coefficients T(n,j) read by rows.at n=36A325220
- a(n) = numerator (2^(4*n-1) * (2^(4*n-2) - 1) * (Bernoulli(4*n-2) / (4*n-2)!) * ((2*n-2)! / Euler(2*n-2))^2).at n=4A334912
- E.g.f. = tan(x).at n=17A350972