199360981

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=14A000111
• Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).at n=7A000364
• Expansion of (1+x)/cos(x).at n=14A009002
• Numerators of Taylor series for sec(x) = 1/cos(x).at n=7A046976
• Numerator of S(n)/Pi^n, where S(n) = Sum_{k=-inf..+inf} (4k+1)^(-n).at n=14A050970
• Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=35A060058
• Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=34A060058
• Triangle A060058 by diagonals.at n=28A060074
• Triangle A060058 by diagonals.at n=29A060074
• Triangle T(n,k) (1 <= k <= n) where the first column (T(n,1)) is the sequence of secant numbers A000364.at n=28A064670
• 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=28A086646
• Numerators of Taylor series for log(tan(x)+1/cos(x)).at n=7A091912
• Numerators of the coefficients in the Taylor expansion of sec(x) + tan(x) around x=0.at n=14A099612
• Denominator of 2*n*A000111(n-1)/A000111(n): approximations of Pi using Euler (up/down) numbers.at n=13A132050
• Triangle read by rows: T(n,k) = value of (d^2n/dx^2n) (tan^(2k)(x)/cos(x)) at the point x = 0.at n=28A151775
• 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=14A163982
• Triangle T(n,m) of the coefficients JacobiDC(x,y) = Sum_{n>=0} Sum_{m=0..n} (-1)^m* T(n,m) *x^(2*n) *y^(2*m)/(2*n)!.at n=28A181612
• 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=21A181613
• Generalized Euler numbers. Square array A(n,k), n >= 1, k >= 0, read by antidiagonals. A(n,k) = n-alternating permutations of length n*k.at n=43A181985
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k cycles that are not up-down. A cycle (b(1), b(2), ...) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1)<b(2)>b(3)<... .at n=35A186361