Quartic means that the "dominant" term is proportional to n^4
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-66 The sequence can be generated by the following quartic: t(n) = (-3n4 + 42n3 - 177n2 - 358n + 2808)/8 for n = 1, 2, 3, ...
The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.
It is possible to find a quartic equation (power 4) so that any fifth number is the next in the sequence. The cubic that fits these is Un = (n3 + 17n + 30)/6 for n = 1, 2, 3, ... and therefore, the next term is 40.
No.
He is known for quartic equations.