A170741 Expansion of g.f.: (1+x)/(1-21*x).

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982, 1498691008824937010622, 31472511185323677223062, 660922734891797221684302

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..756
• Index entries for linear recurrences with constant coefficients, signature (21).

Crossrefs

Cf. A003945.

Programs

GAP

k:=22;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=22; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=22; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

Join[{1}, 22*21^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
Join[{1},NestList[21#&,22,20]] (* Harvey P. Dale, Jul 29 2018 *)

PARI

vector(26, n, k=22; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,22*21**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

Sage

k=22; [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)*22^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 22*21^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (22*exp(21*x) - 1)/21. - G. C. Greubel, Sep 25 2019