A133603 The matrix-vector product A133566 * A000108.

1, 1, 3, 5, 19, 42, 174, 429, 1859, 4862, 21658, 58786, 266798, 742900, 3417340, 9694845, 45052515, 129644790, 607283490, 1767263190, 8331383610, 24466267020, 115948830660, 343059613650, 1632963760974, 4861946401452

Offset

0,3

Comments

A133602 is a companion sequence.

Links

Table of n, a(n) for n=0..25.

Formula

A133566 * A000108 where A133566 = an infinite lower triangular matrix and A000108 = the Catalan sequence. For odd n, a(n) = C(n). For even n, a(n) = C(n) + C(n-1) = A005807(n-1).

Conjecture: n*(n-2)*(3*n-1)*(n+1)*a(n) -8*n*(2*n-3)*a(n-1) -4*(n-1)*(3*n+2)*(

2*n-3)*(2*n-5)*a(n-2)=0. - R. J. Mathar, Jun 20 2015

Example

a(5) = C(5) = 42.
a(6) = 174 = C(6) + C(5) = 132 + 42.

Maple

A133603 := proc(n)
    add(A133566(n+1, k+1)*A000108(k), k=0..n) ;
end proc: # R. J. Mathar, Jun 20 2015

Crossrefs

Cf. A133566, A000108, A133602, A024492 (bisection).

Sequence in context: A242818 A218373 A034511 * A201867 A148534 A148535

Adjacent sequences: A133600 A133601 A133602 * A133604 A133605 A133606

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 18 2007

Status

approved