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A228290 a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n.

%I A228290 #27 Jun 15 2023 13:35:34
%S A228290 0,6,126,1092,5460,19530,55986,137256,299592,597870,1111110,1948716,
%T A228290 3257436,5229042,8108730,12204240,17895696,25646166,36012942,49659540,
%U A228290 67368420,90054426,118778946,154764792,199411800,254313150,321272406,402321276,499738092
%N A228290 a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n.
%H A228290 Alois P. Heinz, <a href="/A228290/b228290.txt">Table of n, a(n) for n = 0..1000</a>
%H A228290 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A228290 G.f.: -6*x*(7*x^4+42*x^3+56*x^2+14*x+1)/(x-1)^7.
%F A228290 a(n) = (n+1)*(n^2+n+1)*a(n-1)/((n-1)*(n^2-3*n+3)) for n>1.
%F A228290 a(1) = 6, else a(n) = (n^7-n)/(n-1).
%F A228290 a(n) = 6*A059721(n) = n*(n+1)*(1+n+n^2)*(1-n+n^2). - _R. J. Mathar_, Aug 21 2013
%F A228290 a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7) for n>6, a(0)=0, a(1)=6, a(2)=126, a(3)=1092, a(4)=5460, a(5)=19530, a(6)=55986. - _Yosu Yurramendi_, Sep 03 2013
%p A228290 a:= n-> (1+(1+(1+(1+(1+n)*n)*n)*n)*n)*n:
%p A228290 seq(a(n), n=0..30);
%p A228290 # second Maple program:
%p A228290 a:= proc(n) option remember; `if`(n<2, 6*n,
%p A228290       (n+1)*(n^2+n+1)*a(n-1)/((n-1)*(n^2-3*n+3)))
%p A228290     end:
%p A228290 seq(a(n), n=0..30);
%p A228290 # third Maple program:
%p A228290 a:= n-> `if`(n=1, 6, (n^7-n)/(n-1)):
%p A228290 seq(a(n), n=0..30);
%o A228290 (R)
%o A228290 a <- c(0, 6, 126, 1092, 5460, 19530, 55986)
%o A228290 for(n in (length(a)+1):30) a[n] <- 7*a[n-1] -21*a[n-2] +35*a[n-3] -35*a[n-4] +21*a[n-5] -7*a[n-6] +a[n-7]
%o A228290 a
%o A228290 [_Yosu Yurramendi_, Sep 03 2013]
%o A228290 (PARI) a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n; \\ _Joerg Arndt_, Sep 03 2013
%Y A228290 Column k=6 of A228275.
%K A228290 nonn,easy
%O A228290 0,2
%A A228290 _Alois P. Heinz_, Aug 19 2013