A014484 - OEIS

%I #14 Jul 11 2018 04:32:06

%S 1,10,112,1440,21120,349440,6451200,131604480,2941747200,71530905600,

%T 1880240947200,53137244160000,1606870263398400,51776930709504000,

%U 1771128112545792000,64103411041173504000

%N Expansion of (1+2x)/(1-2x)^4 (E.g.f.).

%H Robert Israel, <a href="/A014484/b014484.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) = (n+1)(n+2)(2n+3)/6 * 2^n * n!. - _Ralf Stephan_, Mar 24 2004

%F Conjecture: a(n) +(-2*n-9)*a(n-1) +6*(n+1)*a(n-2)=0. - _R. J. Mathar_, Jun 11 2013

%F Conjecture verified by _Robert Israel_, Jul 11 2018

%p seq((n+1)*(n+2)*(2*n+3)/6 * 2^n * n!, n=0..30); # _Robert Israel_, Jul 11 2018

%o (PARI) a(n)=(n+1)*(n+2)*(2*n+3)/6*2^n*n! \\ _Charles R Greathouse IV_, Jun 11 2013

%Y Cf. A006157.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.