A014432 a(n) = Sum_{i=1..n-1} a(i)*a(n-1-i), with a(0) = 1, a(1) = 3.

1, 3, 3, 12, 30, 111, 363, 1353, 4917, 18777, 71769, 280506, 1103556, 4395009, 17622309, 71220828, 289510662, 1183627137, 4862148753, 20061888924, 83100910530, 345457823493, 1440734205513, 6026408186457, 25275954499905, 106277040064191

Offset: 0

Author

Wouter Meeussen

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1545

Crossrefs

Cf. A025237.

Programs

Maple

seq(coeff(convert(series((1+x-sqrt(1-2*x-11*x^2))/(2*x),x,50),polynom),x,i),i=0..30);
A014431:=proc(n) options remember: local i: if n<2 then RETURN([1,3][n+1]) else RETURN(add(A014431(i)*A014431(n-1-i),i=1..n-1)) fi:end;seq(A014431(n),n=0..30); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Mathematica

Rest[CoefficientList[Series[(1+x-Sqrt[1-2x-11x^2])/2,{x,0,30}],x]] (* Harvey P. Dale, Apr 17 2019 *)

PARI

a(n)=polcoeff((1+x-sqrt(1-2*x-11*x^2+x*O(x^n)))/2,n)

Formula

G.f.: ((1+x-sqrt(1-2*x-11*x^2)))/(2*x). - Michael Somos, Jun 08 2000; corrected by Robert Israel, Sep 10 2020

a(n) = (3/(11*n)) * ((3+n)*A025237(n+1) - (2*n+3)*A025237(n)) for n>0. [Mark van Hoeij, Jul 02 2010]

(n+1)*a(n) = (2*n-1)*a(n-1)+11*(n-2)*a(n-2). - Robert Israel, Sep 10 2020

G.f.: 1 + 3*x/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - ...))))) (continued fraction). - Nikolaos Pantelidis, Nov 24 2022

Extensions

Corrected by C. Ronaldo (aga_new_ac(AT)hotmail.com) and Ralf Stephan, Dec 19 2004