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A219314
Composition of the inverse binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers.
1
0, 1, 0, 3, 3, 13, 26, 77, 192, 529, 1412, 3873, 10603, 29315, 81318, 226763, 634627, 1782637, 5022840, 14193457, 40211105, 114191159, 324981030, 926720807, 2647513282, 7576475383, 21716189676, 62336237007, 179182653117, 515717424109, 1486119467026
OFFSET
0,4
FORMULA
G.f.: ((1+2*x)*sqrt(1-2*x-3*x^2) - 1 + x + 2*x^2)/(2*(1+x)*(1-2*x-4*x^2)).
Asymptotics: a(n) ~ 3^(n+2)*5/(8*sqrt(3*Pi*n^3)). - Fung Lam, Apr 07 2014
Conjecture: n*a(n) -2*n*a(n-1) +11*(-n+2)*a(n-2) +4*(2*n-5)*a(n-3) +8*(5*n-17)*a(n-4) +24*(n-4)*a(n-5)=0. - R. J. Mathar, Jun 14 2016
Conjecture: n*(5*n-7)*a(n) -4*(5*n^2-12*n+6)*a(n-1) -(15*n^2-11*n-30) *a(n-2) +2*(35*n^2-119*n+66)*a(n-3) +12*(n-3)*(5*n2)*a(n-4)=0. - R. J. Mathar, Jun 14 2016
CROSSREFS
Sequence in context: A072552 A217246 A186743 * A288146 A019154 A255675
KEYWORD
easy,nonn
AUTHOR
STATUS
approved