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

0,2

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

Links

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

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

Example

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.

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);

Crossrefs

Cf. A125177.

Sequence in context: A221205 A037247 A308273 * A107086 A294790 A234643

Adjacent sequences: A126218 A126219 A126220 * A126222 A126223 A126224

Keyword

nonn

Author

Emeric Deutsch, Dec 28 2006

Status

approved