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A104985 Row sums of triangle A104984.

%I A104985 #7 Jun 08 2021 14:58:09
%S A104985 1,0,-2,-6,-20,-92,-554,-4002,-33096,-306440,-3135766,-35134670,
%T A104985 -427878628,-5628940084,-79572364498,-1203168642362,-19379896959776,
%U A104985 -331331041788640,-5993029816637262,-114348894263852326,-2295445815821635932,-48362099044178487564
%N A104985 Row sums of triangle A104984.
%C A104985 A104984 equals the matrix inverse of A104980.
%H A104985 G. C. Greubel, <a href="/A104985/b104985.txt">Table of n, a(n) for n = 0..445</a>
%F A104985 a(n) = Sum_{k=0..n} A104984(n, k).
%t A104985 A003319[n_]:= A003319[n]= If[n==0, 0, n! -Sum[j!*A003319[n-j], {j,n-1}]];
%t A104985 A104984[n_, k_]:= If[k==n, 1, If[k==n-1, -n, -A003319[n-k]]];
%t A104985 a[n_]:= Sum[A104984[n, k], {k,0,n}];
%t A104985 Table[a[n], {n, 0, 30}] (* _G. C. Greubel_, Jun 07 2021 *)
%o A104985 (PARI) {a(n)=sum(k=0,n,if(k==n,1,if(k==n-1,-n, -polcoeff((1-1/sum(i=0,n-k,i!*x^i))/x+O(x^(n-k)),n-k-1) )))}
%o A104985 (Sage)
%o A104985 @CachedFunction
%o A104985 def T(n,k):
%o A104985     if (k==n): return 1
%o A104985     elif (k==n-1): return -n
%o A104985     else: return -factorial(n-k) - sum( factorial(j)*T(n-k-j, 0) for j in (1..n-k-1) )
%o A104985 [sum(T(n,k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Jun 07 2021
%Y A104985 Cf. A104984, A104980.
%K A104985 sign
%O A104985 0,3
%A A104985 _Paul D. Hanna_, Apr 10 2005