cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A170757 Expansion of g.f.: (1+x)/(1-37*x).

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%I A170757 #19 Sep 08 2022 08:45:49
%S A170757 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A170757 3607411331054,133474219248998,4938546112212926,182726206151878262,
%U A170757 6760869627619495694,250152176221921340678,9255630520211089605086,342458329247810315388182
%N A170757 Expansion of g.f.: (1+x)/(1-37*x).
%H A170757 G. C. Greubel, <a href="/A170757/b170757.txt">Table of n, a(n) for n = 0..634</a>
%H A170757 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (37).
%F A170757 a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*38^k. - _Philippe Deléham_, Dec 04 2009
%F A170757 a(0) = 1; for n>0, a(n) = 38*37^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F A170757 E.g.f.: (1/37)*(38*exp(37*x) - 1). - _Stefano Spezia_, Oct 09 2019
%p A170757 k:=38; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019
%t A170757 With[{k = 38}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)
%o A170757 (PARI) vector(26, n, k=38; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019
%o A170757 (Magma) k:=38; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019
%o A170757 (Sage) k=38; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019
%o A170757 (GAP) k:=38;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 09 2019
%Y A170757 Cf. A003945.
%K A170757 nonn,easy
%O A170757 0,2
%A A170757 _N. J. A. Sloane_, Dec 04 2009