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

1,2

Links

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

N. J. A. Sloane, Transforms

Example

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)))))

Mathematica

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

Crossrefs

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

Sequence in context: A245266 A123897 A351762 * A052693 A050621 A326237

Adjacent sequences: A302354 A302355 A302356 * A302358 A302359 A302360

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2018

Status

approved