Cumulant Generating Function: Definition, Examples

If G(x) is the generating function for the sequence {ak} what is the generating function for each of these sequences? a) 0,0,0, a3, a4, a5, …(assuming that terms follow the pattern of all but the first three terms) b) a0, 0, a1, 0, a2, 0, …c) 0,0,0,0, a0, a1, a2, …(assuming that terms follow the pattern of all but the first four terms) d) a0, 2 a1, 4 a2, 8 a3, 16 a4, …e) 0, a0, a1 / 2, a2 / 3, a3 / 4, …[ Hint: Calculus required here. ] f) a0, a0 a1, a0 a1 a2, a0 a1 a2 a3, … | Numerade

find the generating function for the finite sequence 1 416 64 256 05949

SEQUENCE Function