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A302355 a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of triangular numbers (A000217). 1

%I #6 Apr 06 2018 17:28:46

%S 1,6,72,1390,37515,1307691,56000728,2847503268,167737660533,

%T 11236731677941,843757483026150,70200772129462767,6410711453857626149,

%U 637516967943664853331,68581800216461580653064,7935677122691714769565104,982824624566131043920711329,129722104862557293606783635718

%N a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of triangular numbers (A000217).

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%e The initial coefficients of successive iterations of g.f. A(x) = x/(1 - x)^3 are as follows:

%e n = 1: 0, (1), 3, 6, 10, 15, ... g.f. A(x)

%e n = 2: 0, 1, (6), 30, 137, 588, ... g.f. A(A(x))

%e n = 3: 0, 1, 9, (72), 543, 3933, ... g.f. A(A(A(x)))

%e n = 4: 0, 1, 12, 132, (1390), 14208, ... g.f. A(A(A(A(x))))

%e n = 5: 0, 1, 15, 210, 2840, (37515), ... g.f. A(A(A(A(A(x)))))

%t Table[SeriesCoefficient[Nest[Function[x, x/(1 - x)^3], x, n], {x, 0, n}], {n, 18}]

%Y Cf. A000217, A030280, A119821, A302356.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Apr 06 2018

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Last modified March 29 08:47 EDT 2024. Contains 371267 sequences. (Running on oeis4.)