A025258 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 1, -1, 1, 1.

1, -1, 1, 1, 0, 0, 2, 3, 1, 2, 11, 17, 12, 25, 81, 127, 134, 276, 696, 1118, 1492, 3005, 6607, 10935, 16766, 33047, 67249, 114611, 190706, 369424, 719956, 1258251, 2196855, 4201958, 8000409, 14263679, 25620508, 48585009, 91421253, 165467590

Offset: 1

Author

Clark Kimberling

Keywords

• sign

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3544
• Paul Barry, Riordan Pseudo-Involutions, Continued Fractions and Somos 4 Sequences, arXiv:1807.05794 [math.CO], 2018.

Programs

Mathematica

Nest[Function[a, Append[a, Inner[Times, #1, #2, Plus] & @@ Transpose @@ {Array[{a[[#]], a[[-#]]} &, Length[a] - 2 ]}] ], {1, -1, 1, 1}, 36] (* Michael De Vlieger, Oct 17 2018 *)

Formula

Conjecture: -n*a(n) +(2*n-3)*a(n-1) +3*(-n+3)*a(n-2) +3*(2*n-9)*a(n-3) +(-n+6)*a(n-4)=0. - R. J. Mathar, Feb 25 2015