A302357 a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of Fibonacci numbers (A000045).

1, 2, 12, 102, 1165, 16603, 283283, 5624556, 127309302, 3234191224, 91094448874, 2816800580606, 94848640788603, 3454303753062123, 135278798460362984, 5668566821430630300, 253050028467629998389, 11988740253545762393562

Offset: 1

Author

Ilya Gutkovskiy, Apr 06 2018

Keywords

• nonn

Examples

			The initial coefficients of successive iterations of g.f. A(x) = x/(1 - x - x^2) are as follows:
n = 1: 0, (1), 1,   2,    3,     5,  ... g.f. A(x)
n = 2: 0,  1, (2),  6,   17,    50,  ... g.f. A(A(x))
n = 3: 0,  1,  3, (12),  48,   197,  ... g.f. A(A(A(x)))
n = 4: 0,  1,  4,  20, (102),  532,  ... g.f. A(A(A(A(x))))
n = 5: 0,  1,  5,  30,  185, (1165), ... g.f. A(A(A(A(A(x)))))
		

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000045, A119821, A158832, A270863, A283679.

Programs

Mathematica

Table[SeriesCoefficient[Nest[Function[x, x/(1 - x - x^2)], x, n], {x, 0, n}], {n, 18}]