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%I #6 Mar 30 2012 18:36:58
%S 1,2,12,118,1605,27816,585046,14459138,410368743,13146830110,
%T 469123986529,18447791712945,792514583941223,36925394368325295,
%U 1854525584914459755,99872579714406393286,5740977285851988017769
%N Main diagonal of rectangular table A121424.
%C Also main diagonal of square array A136733.
%F a(n) = [A121412^(n+1)](n,0) for n>=0; i.e., (n+1)-th term of column 0 in matrix power A121412^(n+1).
%o (PARI) {a(n)=local(H=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(H^i)[i-1, j]); )); H=B); return((H^(n+1))[n+1, 1])}
%Y Cf. A121424, A121412.
%Y Cf. A136733; A101483, A121418, A121421.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 26 2006
%E Edited by _N. J. A. Sloane_, Oct 30 2008 at the suggestion of R. J. Mathar