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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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)).

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

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)