A170742 Expansion of g.f.: (1+x)/(1-22*x).

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512, 3148241564354477195264, 69261314415798498295808, 1523748917147566962507776

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..744
• Index entries for linear recurrences with constant coefficients, signature (22).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=23;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=23; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=23; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

With[{k=23}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* G. C. Greubel, Sep 25 2019 *)
LinearRecurrence[{22},{1,23},20] (* Harvey P. Dale, Oct 13 2022 *)

PARI

vector(26, n, k=23; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,23*22**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

Sage

k=23; [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)*23^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 23*22^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (23*exp(22*x) - 1)/22. - G. C. Greubel, Sep 25 2019