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A185676 Riordan array (((1+x)/(1-x-x^2))^m, x*A000108(x)), m=2.

%I A185676 #16 Feb 21 2013 07:29:42
%S A185676 1,4,1,10,5,1,22,16,6,1,45,45,23,7,1,88,121,76,31,8,1,167,325,237,116,
%T A185676 40,9,1,310,895,728,403,166,50,10,1,566,2563,2253,1358,630,227,61,11,
%U A185676 1,1020,7670,7104,4541,2288,930,300,73,12,1,1819,23939,22919,15249,8145,3604,1316,386,86,13,1
%N A185676 Riordan array (((1+x)/(1-x-x^2))^m, x*A000108(x)), m=2.
%F A185676 R(n,k,m) = k*sum(i=0..n-k, sum(j=m..i+m, binomial(j-1,m-1) * binomial(j,i+m-j)) * binomial(2*(n-i)-k-1,n-i-1)/(n-i)), k>0, m=2; R(n,0,m) = sum(i=m..n+m, binomial(i-1,m-1) * binomial(i,n+m-i)).
%e A185676 1;
%e A185676 4,1;
%e A185676 10,5,1;
%e A185676 22,16,6,1;
%e A185676 45,45,23,7,1;
%e A185676 88,121,76,31,8,1;
%e A185676 167,325,237,116,40,9,1;
%e A185676 310,895,728,403,166,50,10,1;
%t A185676 r[n_, k_, m_] := k*Sum[ Sum[ Binomial[j-1, m-1]*Binomial[j, i+m-j], {j, m, i+m}]*Binomial[2*(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]; r[n_, 0, m_] := Sum[ Binomial[i-1, m-1]*Binomial[i, n+m-i], {i, m, n+m}]; Table[r[n, k, 2], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 21 2013 *)
%Y A185676 Column k=0 gives: A004798(n+1).
%K A185676 nonn,tabl
%O A185676 0,2
%A A185676 _Vladimir Kruchinin_, Feb 09 2011