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.
%I A218742 #22 Aug 29 2024 14:31:26
%S A218742 0,1,40,1561,60880,2374321,92598520,3611342281,140842348960,
%T A218742 5492851609441,214221212768200,8354627297959801,325830464620432240,
%U A218742 12707388120196857361,495588136687677437080,19327937330819420046121,753789555901957381798720,29397792680176337890150081
%N A218742 a(n) = (39^n - 1)/38.
%C A218742 Partial sums of powers of 39 (A009983).
%H A218742 Vincenzo Librandi, <a href="/A218742/b218742.txt">Table of n, a(n) for n = 0..600</a>
%H A218742 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218742 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (40,-39).
%F A218742 a(n) = floor(39^n/38).
%F A218742 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218742 G.f.: x/((1-x)*(1-39*x)).
%F A218742 a(n) = 40*a(n-1) - 39*a(n-2). (End)
%F A218742 E.g.f.: exp(20*x)*sinh(19*x)/19. - _Elmo R. Oliveira_, Aug 29 2024
%t A218742 LinearRecurrence[{40, -39}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218742 (39^Range[0,20]-1)/38 (* _Harvey P. Dale_, Mar 05 2023 *)
%o A218742 (PARI) a(n)=39^n\38
%o A218742 (Magma) [n le 2 select n-1 else 40*Self(n-1) - 39*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218742 (Maxima) A218742(n):=(39^n-1)/38$
%o A218742 makelist(A218742(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218742 Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.
%Y A218742 Cf. A009983.
%K A218742 nonn,easy
%O A218742 0,3
%A A218742 _M. F. Hasler_, Nov 04 2012