A170747 Expansion of g.f.: (1+x)/(1-27*x).

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852, 82720755783423343562004, 2233460406152430276174108

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..698
• Index entries for linear recurrences with constant coefficients, signature (27).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=28;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=28; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=28; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

With[{k=28}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* G. C. Greubel, Sep 25 2019 *)

PARI

vector(26, n, k=28; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,28*27**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=28; [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)*28^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n > 0, a(n) = 28*27^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (28*exp(27*x) - 1)/27. - G. C. Greubel, Sep 25 2019