A033589 a(n) = (2*n-1)*(3*n-1)*(4*n-1).
-1, 6, 105, 440, 1155, 2394, 4301, 7020, 10695, 15470, 21489, 28896, 37835, 48450, 60885, 75284, 91791, 110550, 131705, 155400, 181779, 210986, 243165, 278460, 317015, 358974, 404481, 453680, 506715
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(2*n-1)*(3*n-1)*(4*n-1): n in [0..30]]; // G. C. Greubel, Mar 05 2020
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Maple
seq( mul(j*n-1, j=2..4), n=0..30); # G. C. Greubel, Mar 05 2020
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Mathematica
Table[Times@@(n*Range[2,4]-1),{n,0,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{-1,6,105,440},30] (* Harvey P. Dale, Sep 22 2014 *) -
PARI
vector(31, n, my(m=n-1); prod(j=2,4, j*m-1) ) \\ G. C. Greubel, Mar 05 2020
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Sage
[product(j*n-1 for j in (2..4)) for n in (0..30)] # G. C. Greubel, Mar 05 2020
Formula
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Sep 22 2014
G.f.: (-1 +10*x +75*x^2 +60*x^3)/(1-x)^4. - R. J. Mathar, Feb 06 2017
From G. C. Greubel, Mar 05 2020: (Start)
a(n) = n^3 * Pochhammer(2 - 1/n, 3) = Product_{j=2..4} (j*n-1).
E.g.f.: (-1 + 7*x + 46*x^2 + 24*x^3)*exp(x). (End)
Sum_{n>=1} 1/a(n) = (sqrt(3)/2-1)*Pi + 8*log(2) - 9*log(3)/2. - Amiram Eldar, Feb 22 2022