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
Links
- Kenny Lau, Table of n, a(n) for n = 0..733
- Index entries for linear recurrences with constant coefficients, signature (23).
Programs
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GAP
k:=24;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019
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Magma
k:=24; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019
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Maple
k:=24; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019
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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 *) -
PARI
Vec((1+x)/(1-23*x) + O(x^18)) \\ Felix Fröhlich, Aug 02 2017
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Python
for i in range(1001):print(i,24*23**(i-1) if i>0 else 1) # Kenny Lau, Aug 02 2017
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Sage
k=24; [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)*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