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A117399 Column 1 (divided by 2) of triangle A117398, which is the matrix log of A117396.

%I A117399 #7 Sep 07 2022 04:08:26
%S A117399 1,1,2,7,34,202,1402,11122,99322,986362,10784122,128720122,1665516922,
%T A117399 23220588922,347025670522,5534133996922,93802153836922,
%U A117399 1683934185324922,31917365573484922,636941680764780922,13348854673487724922
%N A117399 Column 1 (divided by 2) of triangle A117398, which is the matrix log of A117396.
%H A117399 G. C. Greubel, <a href="/A117399/b117399.txt">Table of n, a(n) for n = 1..250</a>
%t A117399 m=42;
%t A117399 M= Table[If[k>n-1, 0, If[k==n-1, n, -1]], {n,0,m+1}, {k,0,m+1}];
%t A117399 T:= T= Sum[MatrixPower[M, j]/j, {j,m+1}];
%t A117399 Table[T[[n+1, 2]]/2, {n,2,30}] (* _G. C. Greubel_, Sep 06 2022 *)
%o A117399 (PARI) {a(n)=local(M=matrix(n+4,n+4,r,c,if(r>=c,if(r==c+1,-c,1))), L=sum(m=1,n+4,(M^0-M)^m/m));L[n+2,2]/2}
%Y A117399 Cf. A117398, A117396.
%K A117399 nonn
%O A117399 1,3
%A A117399 _Paul D. Hanna_, Mar 11 2006