A012475 a(n) = (2*n+1) [x^(2*n+1)] arctan(cos(x)*sin(x)).

1, -6, 120, -7056, 758400, -130918656, 33173038080, -11587651270656, 5337660866396160, -3134856182239789056, 2286367634020679024640, -2027369655249396662009856, 2147914157998443571728875520, -2679632132940443936986346029056, 3888139806851470107238571232460800

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

A(0,k) = 1 and A(n,k) = -(k*(k+1) * A(n-1,k+2) + 4*k^2 * A(n-1,k)) for n > 0. a(n) = A(n,1). - Seiichi Manyama, Apr 16 2026

Example

arctan(cos(x)*sin(x)) = x - 6/3!*x^3 + 120/5!*x^5 - 7056/7!*x^7 + 758400/9!*x^9 ...

Prog

(PARI) a(n, k=1) = if(n==0, 1, -(k*(k+1)*a(n-1, k+2)+4*k^2*a(n-1, k))); \\ Seiichi Manyama, Apr 16 2026

Crossrefs

Cf. A012477, A028296.

Sequence in context: A012641 A012795 A054479 * A053777 A023199 A355757

Adjacent sequences: A012472 A012473 A012474 * A012476 A012477 A012478

Keyword

sign

Author

Patrick Demichel

Extensions

Definition clarified by Seiichi Manyama, Apr 16 2026

Status

approved