A126221 a(n)=c(n)+c(n-1)+2*c(n-2)+4*c(n-3)+8*c(n-4)+...+2^(n-2)*c(1)+2^(n-1)*c(0), where c(k) are the Catalan numbers (A000108).

1, 2, 5, 13, 35, 98, 286, 869, 2739, 8910, 29754, 101498, 352222, 1239332, 4410204, 15840813, 57344451, 208976022, 765945954, 2821516398, 10439890026, 38781926652, 144580149924, 540737349858, 2028319233390, 7628680720908

Offset: 0

Author

Emeric Deutsch, Dec 28 2006

Keywords

• nonn

Comments

Row sums of A125177.

Equals the eigensequence of a triangle with A000108 as the left border and the rest 1's. - Gary W. Adamson, Jul 24 2010

Examples

			a(4)=35 because c(4)+c(3)+2*c(2)+4*c(1)+8*c(0) = 14+5+2*2+4*1+8*1 = 35.
		

Crossrefs

Cf. A125177.

Programs

Maple

c:=n->binomial(2*n,n)/(n+1): a:=n->c(n)+sum(2^(n-j-1)*c(j),j=0..n-1): seq(a(n),n=0..30);

Formula

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

D-finite with recurrence (n+1)*a(n) +(-7*n+1)*a(n-1) +2*(7*n-8)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jul 22 2022