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