A346174 - OEIS

%I #11 Jul 21 2021 09:17:54

%S 0,1,6,30,120,420,1344,4032,11520,31680,84480,219648,559104,1397760,

%T 3440640,8355840,20054016,47628288,112066560,261488640,605552640,

%U 1392771072,3183476736,7235174400,16357785600,36805017600,82443239424,183911841792,408692981760,904963031040

%N Inverse binomial transform of A317614.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialTransform.html">Binomial Transform</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).

%F O.g.f.: x*(1 - 2*x + 6*x^2 - 8*x^3 + 4*x^4)/(1 - 2*x)^4.

%F E.g.f.: x*(1 + exp(2*x)*(3 + 6*x + 2*x^2))/4.

%F a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 5.

%F a(n) = 2^(n-4)*n*(n + 1)*(n + 2) with a(0) = 0 and a(1) = 1.

%F a(n) = A000079(n-4)*A007531(n+2) for n > 1.

%F a(n) ~ A128789(n)/16.

%F Sum_{n>0} 1/a(n) = 8*log(2) - 13/3 = 1.21184411114622914200452363833...

%t LinearRecurrence[{8,-24,32,-16},{0,1,6,30,120,420},30]

%Y Cf. A000079, A007531, A128789, A257872 (-8*log(2)), A317614.

%K nonn,easy

%O 0,3

%A _Stefano Spezia_, Jul 08 2021