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<a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).
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(MAGMAMagma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 +1386*n^5 +9380*n^4 + 29400*n^3 +41783*n^2 +20874*n +60)/518918400: n in [1..30]]; // G. C. Greubel, Nov 22 2017
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a(n) = Sum_{i=1..n} Cbinomial(i+5,6)^2.
G.f.: x*(1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)/(1-x)^14.
a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 + 1386*n^5 + 9380*n^4 + 29400*n^3 + 41783*n^2 + 20874*n + 60)/518918400. (End)
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(PARI) forvector(n=1, 30, print1(n, sum(i=1, n, binomial(i+5, 6)^2), ", ") ) \\ G. C. Greubel, Nov 22 2017
(Sage) [sum(binomial(j+5, 6)^2 for j in (1..n)) for n in (1..30)] # G. C. Greubel, Aug 27 2019
(GAP) List([1..30], n-> Sum([1..n], j-> Binomial(j+5, 6)^2)); # G. C. Greubel, Aug 27 2019
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