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A025230 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3. 14
3, 1, 6, 37, 234, 1514, 9996, 67181, 458562, 3172478, 22206420, 157027938, 1120292388, 8055001716, 58314533400, 424740506109, 3110401363122, 22888001498102, 169155516667524, 1255072594261142, 9345400450314924 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

G.f.: (1-sqrt(1-12*x+32*x^2))/2 - Michael Somos, Jun 08 2000.

n*a(n) = (12*n-18)*a(n-1) - 32*(n-3)*a(n-2) - Richard Choulet, Dec 17 2009

a(n) ~ 2^(3*n-5/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 11 2013

a(n) = 4^(n-2)*hypergeom([3/2, -n+2], [3], -1) for n>1. - Peter Luschny, Feb 03 2015

a(n+1) = GegenbauerC(n-1, -n, -3)/n for n>=1. - Peter Luschny, May 09 2016

MAPLE

h := n -> simplify(4^n*hypergeom([3/2, -n], [3], -1)):

a := n -> `if`(n=1, 3, h(n-2)):

seq(a(n), n=1..21); # Peter Luschny, Feb 03 2015

MATHEMATICA

Rest[CoefficientList[Series[(1-Sqrt[1-12x+32x^2])/2, {x, 0, 30}], x]]  (* Harvey P. Dale, Feb 22 2011 *)

PROG

(PARI) a(n)=polcoeff((1-sqrt(1-12*x+32*x^2+x*O(x^n)))/2, n)

(PARI) {a(n)=if(n<2, 3*(n==1), n--; polcoeff( serreverse( x/(1+6*x+x^2) +x*O(x^n) ), n))} /* Michael Somos, Oct 14 2006 */

CROSSREFS

Sequence in context: A221929 A157866 A221852 * A152456 A128605 A051511

Adjacent sequences:  A025227 A025228 A025229 * A025231 A025232 A025233

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified March 29 18:39 EDT 2017. Contains 284273 sequences.