A333616 Expansion of x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
0, 1, 3, 6, 6, 10, 10, 15, 15, 21, 21, 28, 28, 36, 36, 45, 45, 55, 55, 66, 66, 78, 78, 91, 91, 105, 105, 120, 120, 136, 136, 153, 153, 171, 171, 190, 190, 210, 210, 231, 231, 253, 253, 276, 276, 300, 300, 325, 325, 351, 351, 378, 378, 406, 406, 435, 435, 465, 465
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
Programs
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Mathematica
LinearRecurrence[{1,2,-2,-1,1},{0,1,3,6,6,10,10,15},59] -
PARI
my(x='x + O('x^59)); concat([0], Vec(serlaplace(((8 + 9*x + x^2)*cosh(x) + (15 + 7*x + x^2)*sinh(x) - 8*(1 + 2*x))/8))) -
Sage
(x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2)).series(x, 59).coefficients(x, sparse=False)
Formula
O.g.f.: x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
E.g.f.: ((8 + 9*x + x^2)*cosh(x) + (15 + 7*x + x^2)*sinh(x) - 8*(1 + 2*x))/8.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 2.
a(n) = A008805(n+1) for n > 2.
Comments