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

Author

Ilya Gutkovskiy, Apr 06 2018

Keywords

• nonn

Examples

			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)))))
		

Links

• N. J. A. Sloane, Transforms
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000217, A030280, A119821, A302356.

Programs

Mathematica

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