A170740 Expansion of g.f.: (1+x)/(1-20*x).

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000, 688128000000000000000, 13762560000000000000000, 275251200000000000000000

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..768
• Index entries for linear recurrences with constant coefficients, signature (20).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=21;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

k:=21; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

Maple

k:=21; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 21*20^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

PARI

vector(26, n, k=21; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

Python

for i in range(31):print(i,21*20**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

Sage

k=21; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*21^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 21*20^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f: (21*exp(20*x) - 1)/20. - G. C. Greubel, Sep 24 2019