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

1, 1, 4, 24, 216, 2540, 36930, 639093, 12821788, 292495896, 7475306400, 211531253076, 6564750305124, 221684308001728, 8091749562745576, 317454163281499140, 13320693233434444092, 595287890670560958740, 28226111104873887744528, 1415312988632326542765024

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..180

Example

Let F_n(x) denote the n-th iteration of F(x) = x + x^2 + x^3;
then coefficients in the successive iterations of F(x) begin:
F_0: [(1), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
F(x):[1, (1), 1, 0, 0, 0, 0, 0, 0, 0, 0, ...];
F_2: [1, 2, (4), 6, 8, 8, 6, 3, 1, 0, 0, ...];
F_3: [1, 3, 9, (24), 60, 138, 294, 579, 1053, 1767, 2739, ...];
F_4: [1, 4, 16, 60, (216), 744, 2460, 7818, 23910, 70446, 200160, ...];
F_5: [1, 5, 25, 120, 560, (2540), 11220, 48330, 203230, 835080, ...];
F_6: [1, 6, 36, 210, 1200, 6720, (36930), 199365, 1058175, ...];
F_7: [1, 7, 49, 336, 2268, 15078, 98826, (639093), 4080531, ...];
F_8: [1, 8, 64, 504, 3920, 30128, 228984, 1722084, (12821788),...];
F_9: [1, 9, 81, 720, 6336, 55224, 477000, 4085028, 34700940, (292495896), ...]; ...
where the coefficients along the diagonal (shown above in parenthesis)
form the initial terms of this sequence.

Prog

(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)))}

Crossrefs

Cf. A166880, A166882, A166883, A166884.

Sequence in context: A323869 A112141 A077555 * A334602 A183279 A145237

Adjacent sequences: A166878 A166879 A166880 * A166882 A166883 A166884

Keyword

nonn

Author

Paul D. Hanna, Oct 22 2009

Extensions

Duplicate a(19) removed by Andrew Howroyd, Feb 22 2018

Status

approved