A174015 A generalized Catalan number sequence.

1, 1, 2, 3, 4, 4, 2, -3, -10, -14, -4, 34, 104, 172, 132, -197, -964, -1976, -2190, 652, 9294, 23626, 33762, 12140, -84438, -280850, -493930, -397666, 639678, 3248466, 6947462, 8068589, -2165978, -35591958, -94129444, -139864826, -56393480, 352505724

Offset

0,3

Comments

Hankel transform is A130151(n+1). First column of A174014.

Links

Table of n, a(n) for n=0..37.

Formula

G.f.: (sqrt(1-2x+x^2+4x^3)+3x-1)/(2x(1-x));

G.f.: 1/(1-x/(1-x/(1+x/(1-x/(1-x/(1+x/(1-... (continued fraction).

a(n) = Sum_{k, 0<=k<=n} A091866(n,k)*(-1)^(n-k) = Sum_{k, 0<=k<=n} A198379(n,k). - Philippe Deléham, Nov 27 2011

Conjecture: (n+1)*a(n) -3*n*a(n-1) +3*(n-1)*a(n-2) +3*(n-4)*a(n-3) +2*(7-2*n)*a(n-4)=0. R. J. Mathar, Nov 13 2012

Crossrefs

Sequence in context: A343835 A307310 A339072 * A014292 A244445 A066078

Adjacent sequences: A174012 A174013 A174014 * A174016 A174017 A174018

Keyword

easy,sign

Author

Paul Barry, Mar 05 2010

Extensions

More terms from Philippe Deléham, Oct 27 2011

Status

approved