cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A302357 #4 Apr 06 2018 17:28:59
%S A302357 1,2,12,102,1165,16603,283283,5624556,127309302,3234191224,
%T A302357 91094448874,2816800580606,94848640788603,3454303753062123,
%U A302357 135278798460362984,5668566821430630300,253050028467629998389,11988740253545762393562
%N A302357 a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of Fibonacci numbers (A000045).
%H A302357 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%e A302357 The initial coefficients of successive iterations of g.f. A(x) = x/(1 - x - x^2) are as follows:
%e A302357 n = 1: 0, (1), 1,   2,    3,     5,  ... g.f. A(x)
%e A302357 n = 2: 0,  1, (2),  6,   17,    50,  ... g.f. A(A(x))
%e A302357 n = 3: 0,  1,  3, (12),  48,   197,  ... g.f. A(A(A(x)))
%e A302357 n = 4: 0,  1,  4,  20, (102),  532,  ... g.f. A(A(A(A(x))))
%e A302357 n = 5: 0,  1,  5,  30,  185, (1165), ... g.f. A(A(A(A(A(x)))))
%t A302357 Table[SeriesCoefficient[Nest[Function[x, x/(1 - x - x^2)], x, n], {x, 0, n}], {n, 18}]
%Y A302357 Cf. A000045, A119821, A158832, A270863, A283679.
%K A302357 nonn
%O A302357 1,2
%A A302357 _Ilya Gutkovskiy_, Apr 06 2018