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Expansion of g.f.: (1+x)/(1-37*x).
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%I #19 Sep 08 2022 08:45:49

%S 1,38,1406,52022,1924814,71218118,2635070366,97497603542,

%T 3607411331054,133474219248998,4938546112212926,182726206151878262,

%U 6760869627619495694,250152176221921340678,9255630520211089605086,342458329247810315388182

%N Expansion of g.f.: (1+x)/(1-37*x).

%H G. C. Greubel, <a href="/A170757/b170757.txt">Table of n, a(n) for n = 0..634</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (37).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*38^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 38*37^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (1/37)*(38*exp(37*x) - 1). - _Stefano Spezia_, Oct 09 2019

%p k:=38; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019

%t With[{k = 38}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)

%o (PARI) vector(26, n, k=38; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019

%o (Magma) k:=38; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019

%o (Sage) k=38; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019

%o (GAP) k:=38;; 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