A170748 Expansion of g.f.: (1+x)/(1-28*x).

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176, 147832005301913337724928

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..690
• Index entries for linear recurrences with constant coefficients, signature (28).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=29;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=29; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=29; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

Join[{1},Table[29*28^(n-1),{n,20}]] (* or *) Join[{1}, NestList[28#&, 29, 20]] (* Harvey P. Dale, Feb 05 2012 *)

PARI

vector(26, n, k=29; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,29*28**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=29; [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)*29^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 29*28^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (29*exp(28*x) -1)/28. - G. C. Greubel, Sep 25 2019