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A061557 a(n) = (7*n+2)*C(n)/(n+2), where C(n) is the n-th Catalan number. 1

%I

%S 3,8,23,70,222,726,2431,8294,28730,100776,357238,1277788,4605980,

%T 16715250,61020495,223931910,825632610,3056887680,11360977650,

%U 42368413620,158498860260,594636663660,2236748680998,8433988655580

%N a(n) = (7*n+2)*C(n)/(n+2), where C(n) is the n-th Catalan number.

%C The identity a(n) = Sum_{k = 0..n} 3*(k-1)*C(k)*C(n-k)/(2*k-1) was verified using the Wilf-Zeilberger theory for hypergeometric sums. The sum arises in the enumeration of separable 1324-avoiding permutations: A026009(n) = a(n)/2 + 2*C(n-1) - 5*C(n)/2.

%C a(n) = 2*C(n+1) - C(n), with C(n) = A000108(n). - _Ralf Stephan_, Jan 13 2004

%Y Cf. A000108, A026009.

%Y A000782 shifted left.

%K easy,nonn

%O 1,1

%A Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001

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Last modified July 5 07:06 EDT 2020. Contains 335460 sequences. (Running on oeis4.)