19391512145
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=16A000111
- Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).at n=8A000364
- Expansion of (1+x)/cos(x).at n=16A009002
- Expansion of e.g.f. Gudermannian(x) = 2*arctan(exp(x)) - Pi/2.at n=8A028296
- Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=43A060058
- Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=44A060058
- Triangle, read by rows, of numbers T(n,k), 0 <= k <= n, given by T(n,k) = A000364(n-k)*binomial(2*n, 2*k).at n=36A086646
- Expansion of e.g.f.: (1+x)*sech(x).at n=16A119882
- Euler (or secant) numbers E(n).at n=16A122045
- Denominator of 2*n*A000111(n-1)/A000111(n): approximations of Pi using Euler (up/down) numbers.at n=15A132050
- Expansion of e.g.f. 2*exp(x)*(1-exp(x))/(1+exp(2*x)).at n=16A163747
- Triangle T(n,m) of the coefficients JacobiNC(x,y) = sum_{n>0} sum_{m=0..n-1} (-1)^m* T(n,m) *x^(2*n) *y^(2*m)/(2*n)!.at n=28A181613
- a(n) = E(n) - E(n+1), where E(n) are the Euler numbers A122045(n).at n=16A241209
- a(2n) = numerator of |Bernoulli(2n)|, a(2n+1) = Euler(2n).at n=17A246006
- Expansion of e.g.f.: sec(x) + 2*tan(x).at n=16A309845
- Number of permutations of [n] with exactly floor(n/2) increasing runs of length two.at n=16A317139
- Number of permutations of [n] with exactly eight increasing runs of even length.at n=0A317288
- The Riordan square of the Euler numbers. Triangle T(n, k), 0 <= k <= n, read by rows.at n=36A321630
- E.g.f.: D(x,k) = 1 + k^2 * Integral S(x,k)*C(x,k)*D(x,k) 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=44A322232
- E.g.f. C(x,y) = cos(y) / sqrt(1 - sin(x)^2 - sin(y)^2).at n=36A324609