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, 6, 72, 1390, 37515, 1307691, 56000728, 2847503268, 167737660533, 11236731677941, 843757483026150, 70200772129462767, 6410711453857626149, 637516967943664853331, 68581800216461580653064, 7935677122691714769565104, 982824624566131043920711329, 129722104862557293606783635718

Offset

1,2

Links

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

N. J. A. Sloane, Transforms

Index to sequences related to polygonal numbers

Example

The initial coefficients of successive iterations of g.f. A(x) = x/(1 - x)^3 are as follows:
n = 1: 0, (1),  3,    6,    10,     15,  ... g.f. A(x)
n = 2: 0,  1,  (6),  30,   137,    588,  ... g.f. A(A(x))
n = 3: 0,  1,   9,  (72),  543,   3933,  ... g.f. A(A(A(x)))
n = 4: 0,  1,  12,  132, (1390), 14208,  ... g.f. A(A(A(A(x))))
n = 5: 0,  1,  15,  210,  2840, (37515), ... g.f. A(A(A(A(A(x)))))

Mathematica

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

Crossrefs

Cf. A000217, A030280, A119821, A302356.

Sequence in context: A001763 A003235 A113133 * A089252 A052730 A010796

Adjacent sequences: A302352 A302353 A302354 * A302356 A302357 A302358

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2018

Status

approved