%I #10 Jun 04 2016 03:36:16
%S 0,5040,12288,22572,36992,56990,84432,121703,171816,238536,326520,
%T 441474,590328,781430,1024760,1332165,1717616,2197488,2790864,3519864,
%U 4410000,5490558,6795008,8361443,10233048,12458600,15093000,18197838
%N Eighth diagonal (m=7) of triangle A084938; a(n) = A084938(n+7,n) = (n^7 + 63*n^6 + 1855*n^5 + 34125*n^4 + 438424*n^3 + 3980172*n^2 + 20946960*n)/5040.
%H Chai Wah Wu, <a href="/A090393/b090393.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A084938(n+7, n) = Sum_{k=0..7} A090238(7, k)*binomial(n, k).
%F From _Chai Wah Wu_, Jun 04 2016: (Start)
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n > 7.
%F G.f.: x*(3447*x^6 - 21824*x^5 + 57742*x^4 - 81760*x^3 + 65388*x^2 - 28032*x + 5040)/(x - 1)^8. (End)
%o (Python)
%o A090393_list, m = [], [1, 6, 25, 92, 327, 1142, 3447, 0]
%o for _ in range(1001):
%o A090393_list.append(m[-1])
%o print(m[-1])
%o for i in range(7):
%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