A026057 a(n) = n*(n^2 + 12*n - 25)/6.
0, -2, 1, 10, 26, 50, 83, 126, 180, 246, 325, 418, 526, 650, 791, 950, 1128, 1326, 1545, 1786, 2050, 2338, 2651, 2990, 3356, 3750, 4173, 4626, 5110, 5626, 6175, 6758, 7376, 8030, 8721, 9450, 10218, 11026, 11875, 12766, 13700, 14678, 15701, 16770, 17886, 19050
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Cf. column 3 of triangle A094415.
Programs
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GAP
List([0..60], n-> n*(n^2+12*n-25)/6); # G. C. Greubel, Oct 30 2019
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Magma
[n*(n^2+12*n-25)/6: n in [0..60]]; // Vincenzo Librandi, Oct 17 2013
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Maple
seq(n*(n^2+12*n-25)/6, n=0..60); # G. C. Greubel, Oct 30 2019
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Mathematica
CoefficientList[Series[x(-2 +9x -6x^2)/(1-x)^4, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 17 2013 *) Table[n (n^2+12n-25)/6,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,-2,1,10},50] (* Harvey P. Dale, Jan 28 2020 *) -
PARI
a(n)=n*(n^2+12*n-25)/6 \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[n*(n^2+12*n-25)/6 for n in (0..60)] # G. C. Greubel, Oct 30 2019
Formula
G.f.: x*(-2 +9*x -6*x^2)/(1-x)^4. - Colin Barker, Sep 17 2012
E.g.f.: x*(-12 +15*x +x^2)*exp(x)/6. - G. C. Greubel, Oct 30 2019
Extensions
New definition from Ralf Stephan, Apr 30 2004
Edited by N. J. A. Sloane, Dec 13 2008
Comments