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

0,2

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

Table of n, a(n) for n=0..20.

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A001792, A006234, A079027, A092288.

Sequence in context: A131435 A209179 A370036 * A079027 A289784 A161727

Adjacent sequences: A081102 A081103 A081104 * A081106 A081107 A081108

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved