A302356 a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of squares (A000290).

1, 8, 123, 3064, 107355, 4880896, 273564907, 18252720536, 1413701944431, 124714304306536, 12347969626724127, 1356049318451627812, 163596640499821625005, 21508738592360523314552, 3060986664449504902865167, 468816798653492762623354936, 76889830949170048691162162275

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)/(1 - x)^3 are as follows:
n = 1: 0, (1),  4,    9,    16,      25,  ... g.f. A(x)
n = 2: 0,  1,  (8),  50,   276,    1397,  ... g.f. A(A(x))
n = 3: 0,  1,  12, (123), 1164,   10420,  ... g.f. A(A(A(x)))
n = 4: 0,  1,  16,  228, (3064),  39542,  ... g.f. A(A(A(A(x))))
n = 5: 0,  1,  20,  365,  6360, (107355), ... g.f. A(A(A(A(A(x)))))
		

Links

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

Crossrefs

Cf. A000290, A030279, A119821, A302355.

Programs

Mathematica

Table[SeriesCoefficient[Nest[Function[x, x (1 + x)/(1 - x)^3], x, n], {x, 0, n}], {n, 17}]