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Expansion of g.f.: (1+x)/(1-31*x).
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%I #26 Sep 08 2022 08:45:49

%S 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,

%T 27292513198112,846067909141472,26228105183385632,813071260684954592,

%U 25205209081233592352,781361481518241362912,24222205927065482250272,750888383739029949758432

%N Expansion of g.f.: (1+x)/(1-31*x).

%H Kenny Lau, <a href="/A170751/b170751.txt">Table of n, a(n) for n = 0..670</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (31).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*32^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 32*31^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (1/31)*(32*exp(31*x) - 1). - _Stefano Spezia_, Oct 09 2019

%p k:=32; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019

%t With[{k = 32}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)

%o (Python) for i in range(1001):print(i,32*31**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

%o (PARI) vector(26, n, k=32; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019

%o (Magma) k:=32; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019

%o (Sage) k=32; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019

%o (GAP) k:=32;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 09 2019

%Y Cf. A003945.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 04 2009