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LinearRecurrence[{5, -10, 10, -5, 1}, {0, 14, 275, 1260, 3705, 8602}, 40] (* Harvey P. Dale, Jan 25 2024 *)
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(PARI) a(n)=max((4*n-3)*(4*n+3)*(2*n+1)*(n+1)/3, 0) \\ Charles R Greathouse IV, Oct 21 2022
nonn,easy
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Wikipedia, <a href="httphttps://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
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seq (a(n), n=0..40);
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Wikipedia, <a href="http://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>