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A062988 a(n) = binomial(n+6,5) - 1.

%I A062988 #27 Apr 25 2024 13:44:57
%S A062988 5,20,55,125,251,461,791,1286,2001,3002,4367,6187,8567,11627,15503,
%T A062988 20348,26333,33648,42503,53129,65779,80729,98279,118754,142505,169910,
%U A062988 201375,237335,278255,324631
%N A062988 a(n) = binomial(n+6,5) - 1.
%C A062988 In the Frey-Sellers reference this sequence is called {(n+2) over 5}_{4}, n >= 0.
%H A062988 Harry J. Smith, <a href="/A062988/b062988.txt">Table of n, a(n) for n = 0..1000</a>
%H A062988 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A062988 a(n) = A062985(n+2, 5).
%F A062988 a(n) = (n+1)*(n^4 + 19*n^3 + 136*n^2 + 444*n + 600)/5!.
%F A062988 G.f.: N(5;1, x)/(1-x)^6 with N(5;1, x)= 5 - 10*x + 10*x^2 - 5*x^3 + x^4 = (1-(1-x)^5)/x, polynomial of second row of A062986.
%F A062988 E.g.f.: (1/120)*(600 + 1800*x + 1200*x^2 + 300*x^3 + 30*x^4 + x^5)*exp(x). - _G. C. Greubel_, Apr 25 2024
%p A062988 [seq(binomial(n+6,5)-1, n=0..35)]; # _Zerinvary Lajos_, Nov 25 2006
%t A062988 Binomial[Range[6,45],5] -1 (* _G. C. Greubel_, Apr 25 2024 *)
%o A062988 (PARI) { for (n=0, 1000, write("b062988.txt", n, " ", binomial(n + 6, 5) - 1) ) } \\ _Harry J. Smith_, Aug 15 2009
%o A062988 (Magma)
%o A062988 [Binomial(n+6,5) -1: n in [0..40]]; // _G. C. Greubel_, Apr 25 2024
%o A062988 (SageMath)
%o A062988 [binomial(n+6,5) -1 for n in range(41)] # _G. C. Greubel_, Apr 25 2024
%Y A062988 Sixth column (r=5) of FS(5) staircase array A062985.
%Y A062988 A column of triangle A014473.
%Y A062988 Cf. A000096, A062748, A063258.
%K A062988 nonn,easy
%O A062988 0,1
%A A062988 _Wolfdieter Lang_, Jul 12 2001