A170743 Expansion of g.f.: (1+x)/(1-23*x).

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416, 6399245651145389894568, 147182649976343967575064

Offset

0,2

Links

Kenny Lau, Table of n, a(n) for n = 0..733

Index entries for linear recurrences with constant coefficients, signature (23).

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*24^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 24*23^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (24*exp(23*x) -1)/23. - G. C. Greubel, Sep 25 2019

Maple

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

Mathematica

CoefficientList[Series[(1+x)/(1-23x), {x, 0, 20}], x] (* or *) LinearRecurrence[ {23}, {1, 24}, 20] (* or *) Join[{1}, NestList[ 23#&, 24, 20]] (* Harvey P. Dale, Oct 21 2015 *)

Prog

(Python) for i in range(1001):print(i, 24*23**(i-1) if i>0 else 1) # Kenny Lau, Aug 02 2017
(PARI) Vec((1+x)/(1-23*x) + O(x^18)) \\ Felix Fröhlich, Aug 02 2017
(Magma) k:=24; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019
(Sage) k=24; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019
(GAP) k:=24;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Crossrefs

Cf. A003945, A097805.

Sequence in context: A170609 A170657 A170705 * A218726 A203487 A007110

Adjacent sequences: A170740 A170741 A170742 * A170744 A170745 A170746

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved