A170753 Expansion of g.f.: (1+x)/(1-33*x).

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469666402, 52073685498991266, 1718431621466711778, 56708243508401488674, 1871372035777249126242, 61755277180649221165986, 2037924146961424298477538

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..658
• Index entries for linear recurrences with constant coefficients, signature (33).

Crossrefs

Cf. A003945.

Programs

GAP

k:=34;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

Magma

k:=34; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

Maple

k:=34; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

Mathematica

With[{k = 34}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

PARI

vector(26, n, k=34; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

Python

for i in range(1001):print(i,34*33**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=34; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*34^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 34*33^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (1/33)*(34*exp(33*x) - 1). - Stefano Spezia, Oct 09 2019