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%I #24 Dec 13 2022 09:54:47
%S 1,2,8,60,816,18480,629280,29806560,1864154880,148459288320,
%T 14652782323200,1754531527795200,250496911136102400,
%U 42032247888401971200,8188505926989625036800,1832839841629043799552000,467088574163459753336832000,134454052266325985991942144000
%N a(n) = n! * (!(n+1)) = n! * Sum_{k=0..n} k!.
%H G. C. Greubel, <a href="/A143217/b143217.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = A000142(n) * A003422(n+1), where A000142 = the factorials and A003422 = partial sums of the factorials. [Corrected by _Georg Fischer_, Dec 13 2022]
%F Equals row sums of triangle A143216.
%e a(4) = 816 = 4! * 34, where 34 = A003422(4) and A000142 = (1, 1, 2, 6, 24, 120, ...).
%e a(4) = 816 = sum of row 4 terms of triangle A143216: (24 + 24 + 48 + 144 + 576).
%t Table[n!*Sum[i!, {i, 0, n}], {n, 0, 16}]
%o (Magma) [Factorial(n)*(&+[Factorial(k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jul 12 2022
%o (SageMath) f=factorial; [f(n)*sum(f(k) for k in (0..n)) for n in (0..40)] # _G. C. Greubel_, Jul 12 2022
%Y Cf. A000142, A003422, A061640.
%Y Cf. A143216, A217238, A217239.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Jul 30 2008
%E Edited and extended by _Olivier Gérard_, Sep 28 2012
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