A133602 The matrix-vector product A133080 * A000108.

1, 2, 2, 7, 14, 56, 132, 561, 1430, 6292, 16796, 75582, 208012, 950912, 2674440, 12369285, 35357670, 165002460, 477638700, 2244901890, 6564120420, 31030387440, 91482563640, 434542177290, 1289904147324, 6151850548776

Offset: 0

Author

Gary W. Adamson, Sep 18 2007

Keywords

• nonn
• easy

Comments

A133603 is a companion sequence.

Examples

			a(4) = C(4) = 14.
a(5) = 56 = C(5) + C(4) = 42 + 14.
		

Crossrefs

Cf. A097806, A133080, A000108, A133603.

Programs

Python

from sympy import catalan
def a005807(n): return catalan(n) + catalan(n + 1)
def a048990(n): return catalan(2*n)
l=[1, 2]
for n in range(2, 31): l+=[a048990(n//2) if n%2==0 else a005807(n - 1)]
print(l) # Indranil Ghosh, Jul 15 2017

Formula

A133080 * A000108, where A133080 = an infinite lower triangular matrix and A000108 = the Catalan sequence as a vector.

a(2n) = A048990(n).

a(2n+1) = A005807(2n).

Conjecture: n*(n-1)*(n-3)*(3*n-4)*a(n) -8*(n-1)*(2*n-5)*a(n-1) -4*(n-2)*(3*n-1)*(2*n-5)*(2*n-7)*a(n-2)=0. - R. J. Mathar, Jun 20 2015