A385897 a(n) = 1 - 5*(n + 1)^2 + 5*(n + 1)^4.
1, 61, 361, 1201, 3001, 6301, 11761, 20161, 32401, 49501, 72601, 102961, 141961, 191101, 252001, 326401, 416161, 523261, 649801, 798001, 970201, 1168861, 1396561, 1656001, 1950001, 2281501, 2653561, 3069361, 3532201, 4045501, 4612801, 5237761, 5924161, 6675901
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Maple
gf := (-x^4 + 4*x^3 - 66*x^2 - 56*x - 1)/(x - 1)^5: ser := series(gf, x, 35): seq(coeff(ser, x, n), n = 0..33);
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Mathematica
a[n_] := With[{h = (n + 1)^2}, 5 (h^2 - h) + 1]; Table[a[n], {n, 0, 33}]
Formula
a(n) = [x^n] (-x^4 + 4*x^3 - 66*x^2 - 56*x - 1)/(x - 1)^5.
a(n) = 5! * [x^5] (1 - sin(n*x))^(-1/n) for n > 0.
a(n) = A385896(n + 5, 5).
A000290(n) = (a(n) - 2*a(n-1) + a(n-2)) / 60.
A008512(n) = (a(n) + 2*a(n-1) + a(n-2)) / 2.
A022521(n) = (a(n-1) + a(n)) / 2.
A061317(n) = (a(n) - a(n-2)) / 20.
A063497(n) = a(n) - a(n-1).
gcd(a(n), a(n+1)) = 1.