The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Jan 09 2025 02:49:32
%S 1,0,-48,-24,1104,1128,-15892,-25368,156240,360640,-1057908,-3600696,
%T 4417678,26438568,-3155508,-144207816,-112109568,564538680,1002957320,
%U -1344487080,-5096138658,-111333800,17182425012,17552839368,-34668142443,-86942440944,4993723500,236551774320
%N A097806^24 * A000594.
%C Conjecture: Given the infinite set of sequences generated from the pairwise operation on A000594 (A097806^k * A000594), k = 24, (A128380) is the only sequence in the set with a zero. The sequence generated from k=23 = (1, -1, -47, 23, 1081, 47, -15939, ...). Analogous conjecture with the partial sum operator: (Cf. A128378, A128379); in which zeros are conjectured to occur only with k=23 and k=24. A128380 mod 24 = 1, 0, 0, 0, 0, 0, -4, 0, 0, 16, ...
%F Pairwise operation performed 24 times on A000594
%t Nest[Prepend[Most[#] + Rest[#], First[#]] &, RamanujanTau[Range[30]], 24] (* _Amiram Eldar_, Jan 08 2025 *)
%Y Cf. A000594, A097806, A128378, A128379.
%K sign
%O 1,3
%A _Gary W. Adamson_, Feb 28 2007
%E More terms from _Amiram Eldar_, Jan 08 2025