A366827 -a(n)/7! is the coefficient of x^7 in the Taylor expansion of the k-th iteration of sin(x).
0, 1, 128, 731, 2160, 4765, 8896, 14903, 23136, 33945, 47680, 64691, 85328, 109941, 138880, 172495, 211136, 255153, 304896, 360715, 422960, 491981, 568128, 651751, 743200, 842825, 950976, 1068003, 1194256, 1330085, 1475840, 1631871, 1798528, 1976161, 2165120, 2365755, 2578416
Offset: 0
Examples
sin(sin(x)) = x - 2*x^3/3! + 12*x^5/5! - 128*x^7/7! + ...; sin(sin(sin(x))) = x - 3*x^3/3! + 33*x^5/5! - 731*x^7/7! + ...; sin(sin(sin(sin(x)))) = x - 4*x^3/3! + 64*x^5/5! - 2160*x^7/7! + ....
Links
- Jianing Song, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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PARI
a(n) = (175/3)*n^3 - 112*n^2 + (164/3)*n
Formula
a(n) = binomial(n,1) + 126*binomial(n,2) + 350*binomial(n,3) = (175*n^2 - 336*n + 164)*n/3. See A366834.
G.f.: x/(1-x)^2 + 126*x^2/(1-x)^3 + 350*x^3/(1-x)^4.
Comments