A170750 Expansion of g.f.: (1+x)/(1-30*x).

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000, 444816117000000000000000

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..676
• Index entries for linear recurrences with constant coefficients, signature (30).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=31;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=31; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=31; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+x)/(1-30x), {x, 0, 25}], x] (* Michael De Vlieger, Aug 04 2017 *)
With[{k = 31}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Sep 25 2019 *)
LinearRecurrence[{30},{1,31},20] (* Harvey P. Dale, Sep 25 2024 *)

PARI

vector(26, n, k=31; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,31*30**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=31; [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)*31^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 31*30^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (31*exp(30*x) - 1)/30. - G. C. Greubel, Sep 25 2019