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

1,1

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

Links

Table of n, a(n) for n=1..24.

Crossrefs

Cf. A000108, A026009.

A000782 shifted left.

Sequence in context: A273716 A184120 A215512 * A000782 A148775 A148776

Adjacent sequences: A061554 A061555 A061556 * A061558 A061559 A061560

Keyword

easy,nonn

Author

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

Status

approved