A171556 a(n) = 3*C(n)-2, where C(n) = A000108(n).

1, 1, 4, 13, 40, 124, 394, 1285, 4288, 14584, 50386, 176356, 624034, 2228698, 8023318, 29084533, 106073008, 388934368, 1432916098, 5301789568, 19692361258, 73398801058, 274447690918, 1029178840948, 3869712441970, 14585839204354

Offset: 0

Author

Paul Barry, Dec 11 2009

Keywords

• easy
• nonn

Comments

Hankel transform is A171557.

Formula

G.f.: 3*(1-sqrt(1-4*x))/(2*x)-2/(1-x).

Starting with offset 1 = Narayana transform (A001263) of [1,3,3,3,...]. - Gary W. Adamson, Jul 29 2011

Conjecture: (n+1)*(n-2)*a(n) +(-5*n^2+11*n-4)*a(n-1) +2*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Sep 30 2012