A265376 a(1) = 1 and a(n) = Sum_{i=1..n-1} (-1)^i*i*a(i).

1, -1, -3, 6, 30, -120, -840, 5040, 45360, -362880, -3991680, 39916800, 518918400, -6227020800, -93405312000, 1307674368000, 22230464256000, -355687428096000, -6758061133824000, 121645100408832000, 2554547108585472000, -51090942171709440000, -1175091669949317120000

Offset: 1

Author

José María Grau Ribas, Dec 07 2015

Keywords

• sign

Comments

1/abs(a(n)) + 1/abs(a(n+1)) = 1/(n-1)!, n = 3,5,7,... hence Sum_{n>1} 1/abs(a(n)) = cosh(1). - Peter McNair, Mar 04 2022

Crossrefs

Cf. A004442, A001710 (b(n)=Sum_{i=1..n-1} i*b(i)).

Programs

Mathematica

a[1]=1; a[n_] := a[n] = Sum[(-1)^i*i*a[i], {i, 1, n - 1}]; Array[a,33]

Formula

For n>1, a(n) = (-1)^floor(n/2) * A001710(n) / floor(n/2). - Vaclav Kotesovec, Jan 26 2016