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%I #12 Jul 20 2016 14:53:29
%S 0,720,1812,3428,5768,9090,13721,20069,28636,40032,54990,74382,99236,
%T 130754,170331,219575,280328,354688,445032,554040,684720,840434,
%U 1024925,1242345,1497284,1794800,2140450,2540322,3001068,3529938,4134815
%N Seventh diagonal (m=6) of triangle A084938; a(n) = A084938(n+6,n) = (n^6 + 45*n^5 + 925*n^4 + 11475*n^3 + 92314*n^2 + 413640*n)/720.
%H Chai Wah Wu, <a href="/A090392/b090392.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F a(n) = A084938(n+6, n) = Sum_{k=0..6} A090238(6, k)*binomial(n, k).
%F From _Chai Wah Wu_, Jun 04 2016: (Start)
%F 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.
%F G.f.: x*(461*x^5 - 2482*x^4 + 5376*x^3 - 5864*x^2 + 3228*x - 720)/(x - 1)^7. (End)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,720,1812,3428,5768,9090,13721},40] (* _Harvey P. Dale_, Jul 20 2016 *)
%o (Python)
%o A090392_list, m = [], [1, 5, 18, 58, 177, 461, 0]
%o for _ in range(1001):
%o A090392_list.append(m[-1])
%o print(m[-1])
%o for i in range(6):
%o m[i+1] += m[i] # _Chai Wah Wu_, Jun 04 2016
%Y Cf. A084938 A090238.
%K easy,nonn
%O 0,2
%A _Philippe Deléham_, Jan 31 2004
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