OFFSET
1,3
COMMENTS
Sign diagram of generating sequence: +++-------------...
The sequences A049171 to A049189 are defined by series reversion of a sequence with rational (ordinary) generating function g(x). Solving g(x)=y for x yields algebraic equations for x, so the sequences have P-finite recurrences. - R. J. Mathar, Jul 24 2023
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
a(n+1) = Sum_{k=0..floor(n/2)} A108759(n,k)*2^k. - Philippe Deléham, Dec 08 2009
Recurrence: 4*(n-1)*n*a(n) = 2*(n-1)*(5*n-6)*a(n-1) + 3*(16*n^2 - 67*n + 69)*a(n-2) + (25*n^2 - 169*n + 285)*a(n-3) + (n-4)*(2*n-9)*a(n-4). - Vaclav Kotesovec, Oct 24 2012
a(n) ~ sqrt(sqrt(3)-1)*((5+3*sqrt(3))/2)^n/(2*sqrt(6*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012
MATHEMATICA
Table[Sum[Binomial[3*k, k]*Binomial[n-1+k, 3*k]/(2k+1)*2^k, {k, 0, Floor[(n-1)/2]}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 24 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
NAME corrected by R. J. Mathar, Jul 23 2023
STATUS
approved