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 A081675 #20 Aug 29 2024 21:10:47 %S A081675 0,1,8,50,286,1566,8358,43870,227606,1170926,5985958,30454590, %T A081675 154371126,780246286,3934789958,19808175710,99577765846,500036345646, %U A081675 2508771728358,12578218511230,63028531771766,315692415197006,1580661100289158,7912101596565150,39595692359108886 %N A081675 Generalized Poly-Bernoulli numbers. %C A081675 Binomial transform of A081674. Second binomial transform of A027649. %H A081675 Vincenzo Librandi, <a href="/A081675/b081675.txt">Table of n, a(n) for n = 0..1000</a> %H A081675 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-38,40). %F A081675 a(n) = (4*5^n - 3*4^n - 2^n)/6. %F A081675 G.f.: x*(1-3*x)/((1-2*x)*(1-4*x)*(1-5*x)). %F A081675 From _Elmo R. Oliveira_, Aug 29 2024: (Start) %F A081675 E.g.f.: exp(2*x)*(4*exp(3*x) - 3*exp(2*x) - 1)/6. %F A081675 a(n) = 11*a(n-1) - 38*a(n-2) + 40*a(n-3) for n > 2. (End) %o A081675 (Magma) [(4*5^n-3*4^n-2^n)/6: n in [0..30]]; // _Vincenzo Librandi_, Jul 17 2011 %Y A081675 Cf. A018678, A027649, A081674. %K A081675 easy,nonn %O A081675 0,3 %A A081675 _Paul Barry_, Mar 28 2003