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

3, 8, 23, 70, 222, 726, 2431, 8294, 28730, 100776, 357238, 1277788, 4605980, 16715250, 61020495, 223931910, 825632610, 3056887680, 11360977650, 42368413620, 158498860260, 594636663660, 2236748680998, 8433988655580

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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.

a(n) = 2*C(n+1) - C(n), with C(n) = A000108(n). - Ralf Stephan, Jan 13 2004

Crossrefs

Cf. A000108, A026009.

A000782 shifted left.