A166882 a(n) = coefficient of x^n in the n-th iteration of (x + x^2 + x^3) for n>=1.

1, 2, 9, 60, 560, 6720, 98826, 1722084, 34700940, 793894860, 20329008975, 576026191026, 17893288364952, 604630781494558, 22079861395250568, 866509034147074284, 36367487433847501620, 1625458443704631873072

Offset: 1

Author

Paul D. Hanna, Oct 22 2009

Keywords

• nonn

Examples

			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, (793894860), ...]; ...
where the coefficients along the diagonal (shown above in parenthesis)
form the initial terms of this sequence.
		

Crossrefs

Cf. A166880, A166881, A166883, A166884.

Programs

PARI

{a(n)=local(F=x+x^2+x^3, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n, G=subst(F, x, G)); return(polcoeff(G, n, x)))}