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a(n) = [x^n] 1 + x*(1 + x*(1 + x*(1 + x*(1 + ...)^(4*n))^(3*n))^(2*n))^n.
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%I #5 Apr 12 2018 05:18:05

%S 1,1,2,21,596,32805,2960496,396523540,73803150440,18216533196693,

%T 5757491981210470,2267526164705341925,1088820552191787545688,

%U 626169526288460672060244,424903177461959840892846066,335946105815409394263421836000,306145042287138023678922165314512

%N a(n) = [x^n] 1 + x*(1 + x*(1 + x*(1 + x*(1 + ...)^(4*n))^(3*n))^(2*n))^n.

%t Table[SeriesCoefficient[1 + x Fold[(x #1 + 1)^(n #2) &, 0, Reverse[Range[n]]], {x, 0, n}], {n, 0, 16}]

%Y Cf. A095793, A138212, A138213, A138214, A138215, A138216, A302657.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 11 2018