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A104991 Row sums of triangle A104990, which equals the matrix cube of triangle A104980.

%I A104991 #7 Jun 08 2021 14:58:28
%S A104991 1,4,22,142,1048,8704,80386,817786,9093340,109794556,1431360958,
%T A104991 20047830262,300343272952,4793871035416,81232799446906,
%U A104991 1456671526257106,27562347560513524,548844246683051860,11474015910364016086
%N A104991 Row sums of triangle A104990, which equals the matrix cube of triangle A104980.
%H A104991 G. C. Greubel, <a href="/A104991/b104991.txt">Table of n, a(n) for n = 0..440</a>
%F A104991 a(n) = Sum_{k=0..n} A104990(n, k).
%t A104991 nmax:=30;
%t A104991 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 A104991 M:= M= With[{q = nmax}, Table[If[j>i, 0, T[i,j]], {i,0,q}, {j,0,q}]];
%t A104991 f:= f= MatrixPower[M, 3];
%t A104991 a[n_]:= a[n]= Sum[f[[n+1, k+1]], {k,0,n}];
%t A104991 Table[a[n], {n, 0, nmax}] (* _G. C. Greubel_, Jun 08 2021 *)
%o A104991 (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))))^-3)[n+1,k+1]))}
%Y A104991 Cf. A104980, A104990.
%K A104991 nonn
%O A104991 0,2
%A A104991 _Paul D. Hanna_, Apr 10 2005