A014431 a(1) = 1, a(2) = 2, a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

1, 2, 2, 6, 14, 42, 122, 382, 1206, 3922, 12914, 43190, 145950, 498170, 1714026, 5940014, 20712646, 72623266, 255875298, 905477734, 3216853294, 11469069258, 41023019098, 147166210014, 529374272470, 1908965352434, 6899707805522, 24991194656022, 90698707816766

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1724

Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.

Formula

a(n) = 2*A025235(n-2) for n>=2.

G.f.: (1+x-sqrt(1-2*x-7*x^2))/2. - Michael Somos, Jun 08 2000

a(n) = (A084601(n) - A084601(n-1))/(2*(n-1)) for n > 1. - Mark van Hoeij, Jul 02 2010

G.f.: x + 2*x^2/G(0) with G(k) = (1 - x - 2*x^2/G(k+1)) (continued fraction). - Nikolaos Pantelidis, Dec 16 2022

Mathematica

Rest@ CoefficientList[Series[(1 + x - Sqrt[1 - 2 x - 7 x^2])/2, {x, 0, 27}], x] (* Michael De Vlieger, Jan 02 2020 *)

Prog

(PARI) a(n)=polcoeff((1+x-sqrt(1-2*x-7*x^2+x*O(x^n)))/2, n)
(Magma) a:=[1, 2]; for n in [3..30] do Append(~a, &+[a[k]*a[n-k]:k in [1..n-2]] ); end for; a; // Marius A. Burtea, Jan 02 2020

Crossrefs

Cf. A025235, A084601.

Sequence in context: A097341 A142710 A369608 * A201687 A259810 A142471

Adjacent sequences: A014428 A014429 A014430 * A014432 A014433 A014434

Keyword

nonn

Author

Clark Kimberling and Wouter Meeussen

Extensions

Corrected by T. D. Noe, Oct 31 2006

Status

approved