A167014 Coefficients of x^n in the (n-1)-th iteration of x/(1-x)^2 for n>=1.

1, 2, 14, 174, 3102, 72090, 2066073, 70420126, 2782399406, 125043232266, 6298621761335, 351484024822788, 21523422229105305, 1434943982960717580, 103463060233836392794, 8022156135358465396630, 665603454632822500855294

Offset: 0

Author

Paul D. Hanna, Oct 28 2009

Keywords

• nonn

Examples

			Let F_n(x) denote the n-th iteration of F(x) = x/(1-x)^2;
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, (2), 3, 4, 5, 6, 7, 8, 9, 10, 11, ...];
F_2: [1, 4, (14), 46, 145, 444, 1331, 3926, 11434, 32960, ...];
F_3: [1, 6, 33, (174), 892, 4480, 22149, 108144, 522685, ...];
F_4: [1, 8, 60, 436, (3102), 21728, 150350, 1030158, 7000917, ...];
F_5: [1, 10, 95, 880, 8015, (72090), 642031, 5671962, ...];
F_6: [1, 12, 138, 1554, 17255, 189596, (2066073), 22361904, ...];
F_7: [1, 14, 189, 2506, 32830, 426244, 5494797, (70420126),...];
F_8: [1, 16, 248, 3784, 57132, 855840, 12740700, 188692708, (2782399406), ...]; ...
where the coefficients along the diagonal (shown in parenthesis)
form the initial terms of this sequence.
		

Crossrefs

Cf. A119821, A119820.

Programs

PARI

{a(n)=local(F=x/(1-x+x*O(x^n))^2, 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)))}