Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #7 Mar 03 2018 23:08:40
%S 1,1,3,11,46,213,1075,5854,34141,211974,1394115,9670976,70501776,
%T 538393812,4294921858,35702077464,308575560999,2767618399029,
%U 25713383197122,247072773486828,2451716229465559,25090920235275889
%N Main diagonal of triangle A129577.
%F Equals first differences (with offset) of column 0 (A129578) of triangle A129577. Equals partial sums (with offset) of row sums (A129580) of triangle A129577.
%F a(n) = Sum_{k=0..n-1} a(k)*C(2*n-k-1,n-k-1)*(k+2)/(n+1) for n>0, with a(0)=1; eigensequence of triangle A033184 when the first column is omitted. - _Paul D. Hanna_, Aug 12 2008
%o (PARI) a(n)=if(n==0,1,sum(k=0,n-1,binomial(2*n-k-1,n-k-1)*(k+2)/(n+1)*a(k))) \\ _Paul D. Hanna_, Aug 12 2008
%Y Cf. A129577, A129578, A129580.
%Y Cf. A033184. - _Paul D. Hanna_, Aug 12 2008
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 24 2007