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A104989 Row sums of triangle A104988, which equals the matrix square of triangle A104980.

%I A104989 #6 Jun 08 2021 15:29:58
%S A104989 1,3,13,69,433,3133,25657,234537,2367825,26176981,314670353,
%T A104989 4088360569,57112939433,853922061413,13609089281849,230346936181465,
%U A104989 4127180489763649,78046835384582069,1553536327234953153
%N A104989 Row sums of triangle A104988, which equals the matrix square of triangle A104980.
%H A104989 G. C. Greubel, <a href="/A104989/b104989.txt">Table of n, a(n) for n = 0..440</a>
%F A104989 a(n) = Sum_{k=0..n} A104988(n, k).
%t A104989 nmax:=30;
%t A104989 T[n_, k_]:= T[n, k] = If[k<0 || k>n, 0, If[k==n, 1, If[k==n-1, n, k*T[n, k+1] + Sum[T[j, 0]*T[n, j+k+1], {j, 0, n-k-1}]]]]; (* T=A104980 *)
%t A104989 M:= M= With[{q = nmax}, Table[If[j>i, 0, T[i,j]], {i,0,q}, {j,0,q}]];
%t A104989 f:= f= MatrixPower[M, 2];
%t A104989 a[n_]:= a[n]= Sum[f[[n+1, k+1]], {k,0,n}];
%t A104989 Table[a[n], {n, 0, nmax}] (* _G. C. Greubel_, Jun 08 2021 *)
%o A104989 (PARI) {a(n)=if(n<0,0,sum(k=0,n,(matrix(n+1,n+1,m,j,if(m==j,1,if(m==j+1,-m+1, -polcoeff((1-1/sum(i=0,m,i!*x^i))/x+O(x^m),m-j-1))))^-2)[n+1,k+1]))}
%Y A104989 Cf. A104980, A104988.
%K A104989 nonn
%O A104989 0,2
%A A104989 _Paul D. Hanna_, Apr 10 2005