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%I #24 Aug 17 2023 11:54:51
%S 5,20,55,125,251,461,791,1286,2001,3002,4367,6187,8567,11627,15503,
%T 20348,26333,33648,42503,53129,65779,80729,98279,118754,142505,169910,
%U 201375,237335,278255,324631
%N a(n) = binomial(n+6,5) - 1.
%C In the Frey-Sellers reference this sequence is called {(n+2) over 5}_{4}, n >= 0.
%H Harry J. Smith, <a href="/A062988/b062988.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F a(n) = A062985(n+2, 5)= (n+1)*(n^4 + 19*n^3 + 136*n^2 + 444*n + 600)/5!.
%F 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.
%p [seq(binomial(n+6,5)-1, n=0..35)]; # _Zerinvary Lajos_, Nov 25 2006
%t s1=s2=s3=s4=0;lst={};Do[a=n+(n+2);s1+=a;s2+=s1;s3+=s2;s4+=s3;AppendTo[lst,s4/2-1],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 04 2009 *)
%o (PARI) { for (n=0, 1000, write("b062988.txt", n, " ", binomial(n + 6, 5) - 1) ) } \\ _Harry J. Smith_, Aug 15 2009
%Y Sixth column (r=5) of FS(5) staircase array A062985.
%Y A column of triangle A014473.
%Y Cf. A000096, A062748, A063258.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jul 12 2001
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