%I #3 Mar 30 2012 18:36:45

%S 1,2,5,12,30,77,202,540,1464,4014,11101,30910,86542,243416,687364,

%T 1947736,5536216,15779646,45088304,129124925,370550378,1065368994,

%U 3068348448,8851297414,25571726480,73981434516,214317561452

%N Main diagonal of triangle A103286, in which row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {2,1}.

%F a(n) ~ 3^n*log_3(n)/(18n) (conjecture).

%o (PARI) {a(n)=local(A=vector(n+1,i,vector(i)),B);A[1][1]=1; for(k=1,n,B=vector(k+1);B[1]=2*A[k][1];B[k+1]=A[k][k]; for(i=2,k,B[i]=2*A[k][i]+A[k][i-1]); A[k+1]=vecsort(B));return(A[n+1][n+1])}

%Y Cf. A103286, A103285.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 28 2005