A081105 5th binomial transform of (1,1,0,0,0,0,.....).

1, 6, 35, 200, 1125, 6250, 34375, 187500, 1015625, 5468750, 29296875, 156250000, 830078125, 4394531250, 23193359375, 122070312500, 640869140625, 3356933593750, 17547607421875, 91552734375000, 476837158203125

Offset: 0

Author

Paul Barry, Mar 07 2003

Keywords

• easy
• nonn

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-25).

Crossrefs

Cf. A001792, A006234, A079027, A092288.

Programs

Mathematica

LinearRecurrence[{10,-25},{1,6},30] (* Harvey P. Dale, Jan 20 2014 *)

PARI

a(n)=if(n,([0,1; -25,10]^n*[1;6])[1,1],1) \\ Charles R Greathouse IV, Oct 07 2015

Formula

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

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

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

a(n) = A079027(n), n>0. - R. J. Mathar, Sep 18 2008

From Amiram Eldar, Jan 19 2021: (Start)

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

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