OFFSET
0,2
COMMENTS
Each second element (which is zero) is skipped. - R. J. Mathar, Mar 10 2016
Annihilating differential operator: (-x^2+432*x^4)*Dx^4 + (-5*x+4320*x^3)*Dx^3 + (-4+10644*x^2)*Dx^2 + 6012*x*Dx + 288.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, Diagonals of rational functions and selected differential Galois groups, arXiv preprint arXiv:1507.03227 [math-ph], 2015
FORMULA
Conjecture: n^3*(2*n-1)*a(n) -6*(4*n-1)*(3*n-1)*(3*n-2)*(4*n-3)*a(n-1)=0. - R. J. Mathar, Mar 10 2016
From Vaclav Kotesovec, Jul 01 2016: (Start)
a(n) = (4*n)! * (3*n)! / ((n!)^3 * (2*n)!^2).
a(n) ~ 2^(4*n - 3/2) * 3^(3*n + 1/2) / (Pi^(3/2) * n^(3/2)).
(End)
0 = (-x^2+432*x^4)*y'''' + (-5*x+4320*x^3)*y''' + (-4+10644*x^2)*y'' + 6012*x*y' + 288*y, where y = 1 + 36*x^2 + 6300*x^4 + ... is the g.f. - Gheorghe Coserea, Jul 03 2016
MAPLE
A268554 := proc(n)
1/(1-w-u*v)/(1-x*y-x*z-y*z) ;
coeftayl(%, x=0, n) ;
coeftayl(%, y=0, n) ;
coeftayl(%, z=0, n) ;
coeftayl(%, u=0, n) ;
coeftayl(%, v=0, n) ;
coeftayl(%, w=0, n) ;
end proc:
seq(A268554(2*n), n=0..40) ; # R. J. Mathar, Mar 10 2016
MATHEMATICA
Table[(4*n)!*(3*n)!/((n!)^3*(2*n)!^2), {n, 0, 15}] (* Vaclav Kotesovec, Jul 01 2016 *)
PROG
(PARI)
my(x1='x1, x2='x2, x3='x3, y1='y1, y2='y2, y3='y3);
R = 1/((1 - y1 - y2*y3) * (1 - x1*x2 - x1*x3 - x2*x3));
diag(n, expr, var) = {
my(a = vector(n));
for (i = 1, #var, expr = taylor(expr, var[#var - i + 1], n));
for (k = 1, n, a[k] = expr;
for (i = 1, #var, a[k] = polcoeff(a[k], k-1)));
return(a);
};
diag(11, R, [x1, x2, x3, y1, y2, y3]) \\ Gheorghe Coserea, Jun 30 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 29 2016
STATUS
approved