Search: id:A128322
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%I A128322
%S A128322 1,3,8,41,234,1602,11976,98541,866942,8139602,80559456,837863578,
%T A128322 9098447188,102867879636,1206145137840,14632952210685,183197674060470,
%U A128322 2362463132266770,31320354882679440,426245968192108590
%N A128322 Column 1 of triangle A128320; a(n) = A128321(n) + 2n*A128321(n-1), where 
               A128321 is column 0 of triangle A128320.
%F A128322 a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2k) 
               where A000108 is the Catalan numbers. a(n) = Sum_{k=0..[(n+1)/2]} 
               C(2(n-k),n-k)/(n-k+1)*C(2k,k)/(k+1)*(k+1)!*C(n+1,2k).
%o A128322 (PARI) {a(n)=sum(k=0,(n+1)\2,binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,
               k)/(k+1) *(k+1)!*binomial(n+1,2*k))}
%Y A128322 Cf. A128320 (triangle), A128321 (column 0), A128323 (column 2), A128324 
               (row sums); variant: A115082.
%Y A128322 Sequence in context: A107991 A007175 A152394 this_sequence A038048 A051763 
               A074435
%Y A128322 Adjacent sequences: A128319 A128320 A128321 this_sequence A128323 A128324 
               A128325
%K A128322 nonn
%O A128322 0,2
%A A128322 Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2007

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