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

0,2

Links

Kenny Lau, Table of n, a(n) for n = 0..756

Index entries for linear recurrences with constant coefficients, signature (21).

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

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 *)

Prog

(Python) for i in range(31):print(i, 22*21**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017
(PARI) vector(26, n, k=22; if(n==1, 1, k*(k-1)^(n-2))) \\ 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
(Sage) k=22; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019
(GAP) k:=22;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Crossrefs

Cf. A003945.

Sequence in context: A170607 A170655 A170703 * A218724 A276644 A139228

Adjacent sequences: A170738 A170739 A170740 * A170742 A170743 A170744

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved