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A302356
a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of squares (A000290).
1
1, 8, 123, 3064, 107355, 4880896, 273564907, 18252720536, 1413701944431, 124714304306536, 12347969626724127, 1356049318451627812, 163596640499821625005, 21508738592360523314552, 3060986664449504902865167, 468816798653492762623354936, 76889830949170048691162162275
OFFSET
1,2
EXAMPLE
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)))))
MATHEMATICA
Table[SeriesCoefficient[Nest[Function[x, x (1 + x)/(1 - x)^3], x, n], {x, 0, n}], {n, 17}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2018
STATUS
approved