OFFSET
0,2
COMMENTS
Binomial transform of A081920.
LINKS
Robert Israel, Table of n, a(n) for n = 0..449
FORMULA
E.g.f. exp(3x)/sqrt(1-x^2)
a(n) = 3^n*n!*Sum_{k=0..floor(n/2)} binomial(2*k, k)/(n-2*k)!/36^k. - Vladeta Jovovic, Oct 11 2003
Conjecture: a(n)-3*a(n-1) -(n-1)^2*a(n-2) +3*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 24 2012
a(n) ~ (exp(6)+(-1)^n)*n^n/exp(n+3). - Vaclav Kotesovec, Oct 05 2013
Mathar's conjecture follows from the differential equation (-3*x^2+x+3)*y+(x^2-1)*y'=0 satisfied by the E.g.f. - Robert Israel, Mar 14 2019
MAPLE
f:= gfun:-rectoproc({a(n)-3*a(n-1)-(n-1)^2*a(n-2)+(3*(n-1))*(n-2)*a(n-3), a(0)=1, a(1)=3, a(2)=10}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Mar 14 2019
MATHEMATICA
CoefficientList[Series[E^(3*x)/Sqrt[1-x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 01 2003
STATUS
approved