A014435 a(n) = Sum_{i=0..n-1} a(i)*a(n-i) with a(0)=1, a(1)=6.

1, 6, 6, 42, 114, 654, 2526, 13506, 61242, 321558, 1579830, 8311578, 42655938, 226373406, 1192341390, 6391471794, 34239385482, 185275416102, 1004459653734, 5480384744202, 29980061984274, 164732303389614, 907579024283454

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f.: ( (1+x)-sqrt(1-2*x-23*x^2) ) / (2*x).

a(n) ~ sqrt((12-sqrt(6))/23) * (1+2*sqrt(6))^(n+1) / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 09 2014

G.f.: 1 + 6*x/G(x) with G(x) = (1 - x - 6*x^2/G(x)) (continued fraction). - Nikolaos Pantelidis, Dec 17 2022

Maple

seq(coeff(convert(series(((1+x)-sqrt(1-2*x-23*x^2))/(2*x), x, 40), polynom), x, i), i=0..25); A014435:=proc(n) options remember: local i: if n<2 then RETURN([1, 6][n+1]) else RETURN(add(A014435(i)*A014435(n-1-i), i=0..n-2)) fi:end; seq(A014435(n), n=0..25); # (C. Ronaldo)

Mathematica

CoefficientList[Series[(1+x-Sqrt[1-2*x-23*x^2])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 09 2014 *)

Crossrefs

Sequence in context: A117859 A229159 A102901 * A175550 A219352 A262895

Adjacent sequences: A014432 A014433 A014434 * A014436 A014437 A014438

Keyword

nonn

Author

Wouter Meeussen

Status

approved