A170746 Expansion of g.f.: (1+x)/(1-26*x).

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352, 45286002241714599985152, 1177436058284579599613952

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..706
• Index entries for linear recurrences with constant coefficients, signature (26).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=27;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=27; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=27; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+x)/(1-26x),{x,0,20}],x] (* or *) Join[ {1}, NestList[26#&,27,20]] (* Harvey P. Dale, Jun 16 2016 *)

PARI

vector(26, n, k=27; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,27*26**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=27; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*27^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 27*26^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (27*exp(26*x) - 1)/26. - G. C. Greubel, Sep 25 2019