Search: id:A128321
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%I A128321
%S A128321 1,1,4,17,98,622,4512,35373,300974,2722070,26118056,263266346,
%T A128321 2780054884,30586452652,349724463584,4141218303165,50678688359190,
%U A128321 639387728054310,8302396672724280,110754894628585950
%N A128321 Column 0 of triangle A128320.
%F A128321 a(n) = Sum_{k=0..[n/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n,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,2k).
%o A128321 (PARI) {a(n)=sum(k=0,n\2,binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,k)/
               (k+1) *(k+1)!*binomial(n,2*k))}
%Y A128321 Cf. A128320 (triangle), A128322 (column 1), A128323 (column 2), A128324 
               (row sums); variant: A115081.
%Y A128321 Sequence in context: A067084 A123750 A024052 this_sequence A091635 A127676 
               A122940
%Y A128321 Adjacent sequences: A128318 A128319 A128320 this_sequence A128322 A128323 
               A128324
%K A128321 nonn
%O A128321 0,3
%A A128321 Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2007

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