A025258 - OEIS

A025258

a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.

%I #9 Oct 17 2018 21:42:32

%S 1,-1,1,1,0,0,2,3,1,2,11,17,12,25,81,127,134,276,696,1118,1492,3005,

%T 6607,10935,16766,33047,67249,114611,190706,369424,719956,1258251,

%U 2196855,4201958,8000409,14263679,25620508,48585009,91421253,165467590

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.

%H Michael De Vlieger, <a href="/A025258/b025258.txt">Table of n, a(n) for n = 1..3544</a>

%H Paul Barry, <a href="https://arxiv.org/abs/1807.05794">Riordan Pseudo-Involutions, Continued Fractions and Somos 4 Sequences</a>, arXiv:1807.05794 [math.CO], 2018.

%F 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

%t 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 *)

%K sign

%O 1,7

%A _Clark Kimberling_