OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..364
FORMULA
a(n) = A000369(n+2,2) = |S2(-3;n+2,2)|, n >= 0.
E.g.f.: d^2/dx^2 ((1-(1-4*x)^(1/4))^2 )/2! = (3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4).
From Robert Israel, Jan 09 2019: (Start)
a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2).
a(n) = 4^(n+1)*(Gamma(n+7/4)/Gamma(3/4) - Gamma(n+3/2)/Gamma(1/2)). (End)
MAPLE
f:= gfun:-rectoproc({a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2), a(0)=1, a(1)=9}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Jan 09 2019
PROG
(PARI) x = 'x + O('x^40); serlaplace((3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4)) \\ Michel Marcus, Jun 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 15 2008
STATUS
approved