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A103285 Main diagonal of triangle A103284, in which row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}.

%I A103285 #7 Nov 19 2015 16:28:46
%S A103285 1,1,2,3,5,9,16,29,53,97,179,333,623,1172,2215,4201,7992,15241,29122,
%T A103285 55745,106879,205223,394637,759973,1465589,2830273,5473068,10597365,
%U A103285 20544860,39876331,77481582,150700968,293380151,571619362,1114581628
%N A103285 Main diagonal of triangle A103284, in which row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}.
%H A103285 Paul D. Hanna, <a href="/A103285/b103285.txt">Table of n, a(n) for n = 0..1000</a>
%F A103285 a(n) ~ 2^n*log_2(n)/(4n).
%o A103285 (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]=1;B[k+1]=A[k][k]; for(i=2,k,B[i]=A[k][i]+A[k][i-1]); A[k+1]=vecsort(B));return(A[n+1][n+1])}
%o A103285 (Haskell)
%o A103285 a103285 = last . a103284_row  -- _Reinhard Zumkeller_, Nov 19 2015
%Y A103285 Cf. A103284.
%K A103285 nonn
%O A103285 0,3
%A A103285 _Paul D. Hanna_, Jan 28 2005