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A166883 a(n) = coefficient of x^n in the (n+1)-th iteration of (x + x^2 + x^3) for n>=1. 4
1, 3, 16, 120, 1200, 15078, 228984, 4085028, 83795085, 1943920935, 50333780640, 1439208976920, 45044270036220, 1531759925038616, 56239576979827360, 2217379518189430404, 93441321290076019236, 4191262657895865499821 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

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(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, ...];

F_10:[1, 10, 100, 990, 9720, 94680, 915390, 8787735, (83795085), ...]; ...

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, A166881, A166882, A166884.

Sequence in context: A200318 A120015 A003692 * A145158 A132070 A121629

Adjacent sequences:  A166880 A166881 A166882 * A166884 A166885 A166886

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 22 2009

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)