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Partial sums of A128379.
6

%I #11 Jan 09 2025 02:45:39

%S 1,0,-24,-24,252,552,-1196,-5496,-1218,27808,50532,-44136,-286534,

%T -305256,551724,2023976,1639485,-3659784,-11484752,-9396720,16258722,

%U 55073200,55004040,-44731872,-220443155,-289179552,5590128,691963304,1254552228,741227832,-1414045956

%N Partial sums of A128379.

%C Conjecture: Given the infinite set of sequences generated from using the partial sum operator on A000594, (i.e. A000012^k * A000594, k in succession = 1, 2, 3, ...), k = 23 and k = 24 are the only two sequences in the set with zeros. In A128379, k = 23: (1, -1, -24, 0, 276, 300, -1748, -4300, ...).

%F A000012^24 * A000594; (partial sum operator performed 24 times on A000594).

%t Nest[Accumulate, RamanujanTau[Range[32]], 24] (* _Amiram Eldar_, Jan 08 2025 *)

%Y Cf. A000012, A000594, A128379.

%K sign

%O 1,3

%A _Gary W. Adamson_, Feb 28 2007