2702765

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=12A000111
• Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).at n=6A000364
• Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.at n=36A008294
• Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of length at least 2.at n=41A008971
• Expansion of (1+x)/cos(x).at n=12A009002
• Apply partial sum operator 4 times to partition numbers.at n=30A014161
• Expansion of e.g.f. Gudermannian(x) = 2*arctan(exp(x)) - Pi/2.at n=6A028296
• Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=26A060058
• Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).at n=27A060058
• Triangle of coefficients of certain polynomials used for G.f.s of columns of triangle A060058.at n=21A060063
• Triangle A060058 by diagonals.at n=21A060074
• Triangle A060058 by diagonals.at n=22A060074
• Triangle T(n,k) (1 <= k <= n) where the first column (T(n,1)) is the sequence of secant numbers A000364.at n=21A064670
• 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=21A086646
• Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.at n=27A086872
• Triangle T(n,k), read by rows, given by A000290 DELTA [1, 2, 6, 5, 11, 8, 16, 11, 21, 14, 26, 17, 31, 20, 36, ...] where DELTA is the operator defined in A084938.at n=29A088969
• Triangle read by rows: T(n,k) is the number of down-up permutations on [n] with k left-to-right maxima.at n=42A098906
• Expansion of e.g.f.: (1+x)*sech(x).at n=12A119882
• Euler (or secant) numbers E(n).at n=12A122045
• Variant of triangle A008301, read by rows of 2*n+1 terms, such that the first column is the secant numbers (A000364).at n=36A125053