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A166881 a(n) = coefficient of x^n in the (n-1)-th iteration of (x + x^2 + x^3) for n>=1.

%I A166881 #10 Feb 22 2018 20:24:25
%S A166881 1,1,4,24,216,2540,36930,639093,12821788,292495896,7475306400,
%T A166881 211531253076,6564750305124,221684308001728,8091749562745576,
%U A166881 317454163281499140,13320693233434444092,595287890670560958740,28226111104873887744528,1415312988632326542765024
%N A166881 a(n) = coefficient of x^n in the (n-1)-th iteration of (x + x^2 + x^3) for n>=1.
%H A166881 Paul D. Hanna, <a href="/A166881/b166881.txt">Table of n, a(n) for n = 1..180</a>
%e A166881 Let F_n(x) denote the n-th iteration of F(x) = x + x^2 + x^3;
%e A166881 then coefficients in the successive iterations of F(x) begin:
%e A166881 F_0: [(1), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
%e A166881 F(x):[1, (1), 1, 0, 0, 0, 0, 0, 0, 0, 0, ...];
%e A166881 F_2: [1, 2, (4), 6, 8, 8, 6, 3, 1, 0, 0, ...];
%e A166881 F_3: [1, 3, 9, (24), 60, 138, 294, 579, 1053, 1767, 2739, ...];
%e A166881 F_4: [1, 4, 16, 60, (216), 744, 2460, 7818, 23910, 70446, 200160, ...];
%e A166881 F_5: [1, 5, 25, 120, 560, (2540), 11220, 48330, 203230, 835080, ...];
%e A166881 F_6: [1, 6, 36, 210, 1200, 6720, (36930), 199365, 1058175, ...];
%e A166881 F_7: [1, 7, 49, 336, 2268, 15078, 98826, (639093), 4080531, ...];
%e A166881 F_8: [1, 8, 64, 504, 3920, 30128, 228984, 1722084, (12821788),...];
%e A166881 F_9: [1, 9, 81, 720, 6336, 55224, 477000, 4085028, 34700940, (292495896), ...]; ...
%e A166881 where the coefficients along the diagonal (shown above in parenthesis)
%e A166881 form the initial terms of this sequence.
%o A166881 (PARI) {a(n)=local(F=x+x^2+x^3, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n-1, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
%Y A166881 Cf. A166880, A166882, A166883, A166884.
%K A166881 nonn
%O A166881 1,3
%A A166881 _Paul D. Hanna_, Oct 22 2009
%E A166881 Duplicate a(19) removed by _Andrew Howroyd_, Feb 22 2018