%I #24 Jan 19 2021 05:49:22

%S 1,6,35,200,1125,6250,34375,187500,1015625,5468750,29296875,156250000,

%T 830078125,4394531250,23193359375,122070312500,640869140625,

%U 3356933593750,17547607421875,91552734375000,476837158203125

%N 5th binomial transform of (1,1,0,0,0,0,.....).

%C Main diagonal of array defined by m(1,j)=j; m(i,1)=i and m(i,j)=m(i-1,j)+4*m(i-1,j-1) - _Benoit Cloitre_, Jun 13 2003

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-25).

%F a(n) = 10*a(n-1)-25*a(n-2), a(0)=1, a(1)=6.

%F a(n) = (n+5)*5^(n-1).

%F G.f.: (1-4x)/(1-5x)^2.

%F a(n) = A079027(n), n>0. - _R. J. Mathar_, Sep 18 2008

%F From _Amiram Eldar_, Jan 19 2021: (Start)

%F Sum_{n>=0} 1/a(n) = 15625*log(5/4) - 41825/12.

%F Sum_{n>=0} (-1)^n/a(n) = 15625*log(6/5) - 34175/12. (End)

%t LinearRecurrence[{10,-25},{1,6},30] (* _Harvey P. Dale_, Jan 20 2014 *)

%o (PARI) a(n)=if(n,([0,1; -25,10]^n*[1;6])[1,1],1) \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A001792, A006234, A079027, A092288.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 07 2003