A128381 - OEIS

%I #11 Jan 09 2025 02:50:26

%S 1,0,-324,-10976,-260898,-4919184,-67536616,-212659776,28757879829,

%T 1419855850728,48139832128404,1387340166285216,36039677403855158,

%U 861269016060967824,18976682736434056968,379832429643337648960,6586595998856413482930,83878202724395340243384,7117837083803882256428

%N A007318^24 * A000594.

%C Conjecture: given the bto performed any k times on A000594 (k = 1, 2, 3, ...); k = 6 and k = 24 are the only members of the set with zeros. k = 6 generates (1, -18, 0, 688, 4494, 5508, ...).

%F Binomial transform operation performed 24 times on A000594, assuming A000594 has offset zero.

%t Nest[Table[Sum[Binomial[n-1, k-1] * #[[k]], {k, 1, n}], {n, 1, Length[#]}] &, RamanujanTau[Range[19]], 24] (* _Amiram Eldar_, Jan 08 2025 *)

%Y Cf. A007318, A000594, A128378, A128379, A128380, A128382.

%K sign

%O 0,3

%A _Gary W. Adamson_, Feb 28 2007