A014483 Expansion of (1+2*x) / (1-2*x)^4.
1, 10, 56, 240, 880, 2912, 8960, 26112, 72960, 197120, 518144, 1331200, 3354624, 8314880, 20316160, 49020928, 116981760, 276430848, 647495680, 1504706560, 3471835136, 7958691840, 18136170496, 41104179200, 92694118400, 208071032832, 465064427520
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
Programs
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PARI
Vec((1 + 2*x) / (1 - 2*x)^4 + O(x^30)) \\ Charles R Greathouse IV, Sep 26 2012, corrected by Colin Barker, Feb 13 2017
Formula
a(n) = 2^n * A000330(n+1). - R. J. Mathar, Oct 23 2008
From Colin Barker, Feb 13 2017: (Start)
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>3.
a(n) = (2^(n-1)*(6 + 13*n + 9*n^2 + 2*n^3)) / 3. (End)
a(n) = (1/2) * Sum_{k=0..n+1} Sum_{i=0..n+1} (n-i+1)^2 * C(n+1,k). - Wesley Ivan Hurt, Sep 21 2017
Extensions
More terms from Colin Barker, Feb 13 2017